Think about that; if the planes are not parallel, they must intersect, eventually. If two lines intersect at a point, then the shortest distance between is 0. The shortest distance between two parallel lines is equal to determining how far apart lines are. 7r1 + 11r2 = 0                                              ……(4). (2,2,−6)| |h2,2,−6i| = 4 √ 44. Distance Between Two Parallel Planes. Distance between two Parallel Lines . Shortest Distance between two lines. p2. Also find the shortest distance between the two. )∣/∣b∣. For two non-intersecting lines lying in the same plane, the shortest distance is the distance that is shortest of all the distances between two points lying on both lines. So far my approach has been as follow: I have chosen some reference z values and recalculated all the deltas for both lines to these reference z values. We want to find the w(s,t) that has a minimum length for all s and t. This can be computed using calculus [Eberly, 2001]. We are going to calculate the distance between the straight lines: $$r:x-2=\dfrac{y+3}{2}=z \qquad r':x=y=z$$$First we determine its relative position. In the usual rectangular xyz-coordinate system, let the two points be P 1 a 1,b 1,c 1 and P 2 a 2,b 2,c 2 ; d P 1P 2 a 2 " a 1,b 2 " b 1,c 2 " c 1 is the direction vector from P 1 to P 2. 5x+4y+3z= 8 and 5x+4y+ 3z= 1 are two parallel planes. distance formula between two points examples, We may derive a formula using this approach and use this formula directly to find the shortest distance between two parallel lines. “Relax, we won’t flood your facebook In this section, we shall discuss how to find the distance between two parallel lines. The path much travel from point A to B to C. A and C are fixed points in 3D space. Keywords: Math, shortest distance between two lines The distance between two lines in $$\mathbb R^3$$ is equal to the distance between parallel planes that contain these lines. Email, Please Enter the valid mobile Shortest distance between two lines and Equation. This approach works well when the lines are relatively vertical, but it fails when the lines are going horizontally, especially when they have undulations Before we proceed towards the shortest distance between two lines, we first try to find out the distance formula for two points. In Class 11, we studied basics of Three Dimensional Geometry - Like Distance Formula, Section Formula . \qquad r':\left\{ \begin{array}{l} x-y=0 \\ x-z=0 \end{array} \right.$$Consider two lines L 1: and L 2: . Solution of I. To find a step-by-step solution for the distance between two lines. Homework Statement how to write the vector equation of the line of shortest distance between two skew lines in the shortest and most efficient way? Thanks Harrow, and yes I think too it needs a macro. Hey guys, I have two lines with two different parametric equations. In other words, it is the shortest distance between them, and hence the answer is 5 5 5. (\vec {b}_1 \times \vec {b}_2) | / | \vec {b}_1 \times \vec {b}_2 | d = ∣(a2. The distance between these points is 3 4 2. Now we discuss the condition for non-intersecting lines. Signing up with Facebook allows you to connect with friends and classmates already Shortest distance between two lines. Skew Lines. If two lines are parallel, then the shortest distance between will be given by the length of the perpendicular drawn from a point on one line form another line. def distance_from_two_lines(e1, e2, r1, r2): # e1, e2 = Direction vector # r1, r2 = Point where the line passes through # Find the unit vector perpendicular to both lines n = np.cross(e1, e2) n /= np.linalg.norm(n) # Calculate distance d = np.dot(n, r1 - r2) return d In order to find the distance between two parallel lines, first we find a point on one of the lines and then we find its distance from the other line. If they intersect, then at that line of intersection, they have no distance -- 0 distance -- between them. Before we proceed towards the shortest distance between two lines, we first try to find out the distance formula for two points. news feed!”. Distance between Lines. If there are two points say A(x 1, y 1) and B(x 2, y 2), then the distance between these two points is given by √[(x 1-x 2) 2 + (y 1-y 2) 2]. You may be asked to find the distance between two points on the test, but not between two lines. Given two lines and , we want to find the shortest distance. L 1 = (x+1)/3 = (y+2)/1 = (z+1)/2. Find the unit vector perpendicular to both L1 and L2. Media Coverage | Skew lines are the lines which are neither intersecting nor parallel. I was using your formula to find the distance between lines y=-3x+10 and y=-3+2. | \vec {PT} |. Can be a vector of two numbers, a matrix of 2 columns (first one is longitude, second is latitude) or a SpatialPoints* object. I have been looking for a solution for hours, but all of them seem to work with lines rather than line segments. This thread is locked. Think about that; if the planes are not parallel, they must intersect, eventually. There will be a point on the first line and a point on the second line that will be closest to each other. It does not matter which perpendicular line you are choosing, as long as two points are on the line. To do it we must write the implicit equations of the straight line:$$$ r:\left\{ \begin{array}{l} 2x-y-7=0 \\ x-z-2=0 \end{array} \right. Shortest distance between a point and a plane. What happens with this sign, when P and Qare interchanged? The points on the parabolas where the tangents have gradient 1 are ( 1 2, 5 4) on x 2 = y − 1, and ( 5 4, 1 2) on y 2 = x − 1. and on line (2) is Q (x2 + l2r2, y2 + m2r2, z2 + n2r2). This concept teaches students how to find the distance between parallel lines using the distance formula. Ex 11.2, 15 - Find shortest distance between lines - 3D Geometry Ex 11.2, 15 (Cartesian method) Find the shortest distance between the lines ( + 1)/7 = ( + 1)/(− 6) = ( + 1)/1 and ( − 3)/1 = ( − 5)/(− 2) = ( − 7)/1 Shortest distance between two lines https://skydrive.live.com/redir?resid=6D7256C9372AD3C0!6331&authkey=!ABaVUe7yN85COj0. In the image describe the line with start and end point. thanks to all the guys who took the time to help me. Refund Policy, Register and Get connected with IITian Mathematics faculty, Please choose a valid in the horizontal section. So far my approach has been as follow: I have chosen some reference z values and recalculated all the deltas for both lines to these reference z values. reference plane at a certain depth "z" and calculating the distance between the lines on each reference plane). Formula Online space geometric calculator to find the shortest distance between given two lines in space, each passing through a point and parallel to a vector. It can be done without it for a small amount of points, but not when you have 100'd of them and this it is not smth that you can record. I got great help from Lars Ake, Andrea Killer, Bernie Deitrick. –a1. Volume of a tetrahedron and a parallelepiped. Shortest Distance Between Parallel LinesWatch more videos at https://www.tutorialspoint.com/videotutorials/index.htmLecture By: Er. Given are the initial starting coordinates, the additional measurement points (represented below as deltas) and the total measured lengths of two lines in space in the following form: The deltas are measured in irregular distances and have different values (in the same line and from line to line). For example, the equations of two parallel lines If two lines are parallel, then the shortest distance between will be given by the length of the perpendicular drawn from a point on one line form another line. To find a step-by-step solution for the distance between two lines. I want to calculate the closest distance between the two lines and I also want to know where it happens (z2+delta). Illustration: Consider the lines. (The exact lines given in a particular problem in my book can be referenced- L1=(3i+8j+3k)+λ(3i-j+k) and L2=(-3i … = ∣b × (a2. Various Recommended Books of Mathematics are just a click away. I have chosen some reference z values and recalculated all the deltas for both lines to these reference z values. Thus, the distance between two parallel lines is given by –. To find that distance first find the normal vector of those planes - it is the cross product of directional vectors of the given lines. The distance between two parallel planes is understood to be the shortest distance between their surfaces. Let's try two different points on the line y = 2 x + 5 y = 2x + 5 y = 2 x + 5. I have two line segments: X1,Y1,Z1 - X2,Y2,Z2 And X3,Y3,Z3 - X4,Y4,Z4. , Cartesian to Spherical coordinates. ∴ Equation of shortest distance line is. Such form of equation is also termed as the unsymmetrical form. It’s an easier way as well. as above; or missing, in which case the sequential distance between the points in p1 is computed. For example, the equations of two parallel lines = | { \vec {b} \times (\vec {a}_2 – \vec {a}_1 ) } | / | \vec {b}| ∣P T ∣. Clearly, any general point on this line at a distance ‘k’ from the point A(x1, y1, z1) is given by P(x1 + lk, y1 + mk, z1 + nk). Ian thank you very much for the formula for the shortest distance between 2 parrelel lines, the formula will help me in the future. I want to calculate the closest distance between the two lines and I also want to know where it happens (z2+delta). Cartesian to Cylindrical coordinates. Shortest Distance Between Two Lines formula. Contact Us | I already have start and end point for both lines but I am not getting any idea how to calculate the minimum distance between two lines. Euclidean Plane formulas list online. On solving equations (3) and (4), we get r1 = r2= 0. The shortest distance between the two parallel lines can be determined using the length of the perpendicular segment between the lines. Remark: If any straight line is given in general form then it can be transformed into symmetrical form and we can further proceed. Hence, the required unit vector is (-i-7j+5k)/√[(-1)2 + (-7)2 + (5)2], The shortest distance between L1 and L2 is, |[(2-(-1))i + (2-2)j + (3-(-1))k] . If there are two points say A(x1, y1) and B(x2, y2), then the distance between these two points is given by √[(x1-x2)2 + (y1-y2)2]. L 2 = (x-2)/1 = (y+2)/2 = (z-3)/3. Subsequently he points P and Q can be found. If PQ is line of shortest distance, then direction ratios of PQ, = (3r1 + 3) – (–3 – 3r2), (8 – r1) – (2r2 – 7), (r1+ 3) – (4r2 + 6), i.e. It provides assistance to avoid nerve wrenching manual calculation followed by distance equation while calculating the distance between points in space. I am not able to find it anymore. This means that we have, ∣ P T ⃗ ∣. Ex 11.2, 14 Find the shortest distance between the lines ⃗ = ( ̂ + 2 ̂ + ̂) + ( ̂ − ̂ + ̂) and ⃗ = (2 ̂ − ̂ − ̂) + (2 ̂ + ̂ + 2 ̂) Shortest distance between the lines with vector equations ⃗ = (1) ⃗ + (1) ⃗and ⃗ = (2) ⃗ + (2) ⃗ is The formula for calculating it can be derived and expressed in several ways. We already have (5,1) that is not located on the line y = 3x + 2. The shortest distance between two parallel lines is the length of the perpendicular segment between them. And I was asked to find the shortest distance between the two lines. Therefore, distance between the lines (1) and (2) is |(–m)(–c1/m) + (–c2)|/√(1 + m2) or d = |c1–c2|/√(1+m2). Answer to: Find the shortest distance between the lines ~x,y,z = ~1,0,4 + t~1,3,-1 and ~x,y,z = ~0,2,0 + s~2,1,1. The formula for calculating it can be derived and expressed in several ways. d = ∣ ( a ⃗ 2 – a ⃗ 1). The distance between two skew lines is naturally the shortest distance between the lines, i.e., the length of a perpendicular to both lines. View the following video for more on distance formula: A straight line in space is characterized by the intersection of two planes which are not parallel and hence the equation of straight line is in fact the solution of the system consisting of the equation of the planes: a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 = 0. Could we have a link to the folder? Since, the vector is perpendicular to both L1 and L2 and so by solving with the help of determinants we obtain it as -i-7j+5k. The shortest distance between two skew lines lies along the line which is perpendicular to both the lines. But wait, wouldn't you get a different result if you try different points? Two lines are called non intersecting if they do not lie in the same plane. (x – 3)/3 = (y – 8)/–1 = (z– 3)/1 = r1 (say)          ……(1), (x + 3)/–3 = (y +7)/2 = (z – 6)/4 = r2 (say)          ……(2), Any point on line (1) is of the form P (3r1 + 3, 8 – r1, r1 + 3). Euclidean Plane formulas list online. Cartesian to Spherical coordinates. Privacy Policy | Shortest distance between a point and a plane. How to Find Find shortest distance between two lines and their Equation. Register yourself for the free demo class from = ∣ b ⃗ × ( a ⃗ 2 – a ⃗ 1 ) ∣ / ∣ b ⃗ ∣. distance formula between two points examples, longitude/latitude of point(s). Thanks for your feedback, it helps us improve the site. Formula to find distance between two parallel line: Consider two parallel lines are represented in the following form : y = mx + c 1 …. I am trying to find the shortest distance between the two segments. Solutions of all questions and examples with formula sheet explained. It doesn’t matter which perpendicular line you choose, as long as the two points are on the lines. . You can follow the question or vote as helpful, but you cannot reply to this thread. This can be done by measuring the length of a line that is perpendicular to both of them. Find the unit vector perpendicular to both L 1 and L 2. Well, you probably recognize the formula in a two-dimensional space: $d = \sqrt{x^2+y^2}$ That's the length straight line between the two points, on a flat plane. Spherical to Cylindrical coordinates. The line1 is passing though point A (a 1 ,b 1 ,c 1 ) and parallel to vector V 1 and The line2 is passing though point B(a 2 ,b 2 ,c 2 ) and parallel to vector V 2 . We may derive a formula using this approach and use this formula directly to find the shortest distance between two parallel lines. Solution of I. B is a point located somewhere on the line segment DE. Iniitally I looked for help in excel forum and then in VBA programing forum. Use Coupon: CART20 and get 20% off on all online Study Material, Complete Your Registration (Step 2 of 2 ), Live 1-1 coding classes to unleash the creator in your Child, Shortest Distance Between Two Non-Intersecting Lines. Question to the reader: also here, without the absolute value, the formula can give a negative result. ( b ⃗ 1 × b ⃗ 2) ∣ / ∣ b ⃗ 1 × b ⃗ 2 ∣. Skipping the details, I need to find an algorithm for finding the shortest distance between three points along a line segment. Can this be done without a macro, because I do not know how to write a macro. using askIItians. Then, the shortest distance between the two skew lines will be the projection of PQ on the normal, which is given by. p2. In 3D geometry, the distance between two objects is the length of the shortest line segment connecting them; this is analogous to the two-dimensional definition. This is a great problem because it uses all these things that we have learned so far: Look into the past year papers to get an idea about the types of questions asked in the exam. 3r1 + 3r2 + 6, –r1 – 2r2 + 15, r1 – 4r2 – 3, As PQ is perpendicular to lines (1) and (2), ∴ 3(3r1 + 3r2 + 6) – 1(–r1 – 2r2 + 15) + 1(r1 – 4r2 - 3) = 0, ⇒11r1 + 7r2 = 0                                              ……(3), and –3(3r1 + 3r2 + 6) + 2(–r1 – 2r2 + 15) + 4(r1 – 4r2 - 3) = 0, i.e. Then, the formula for shortest distance can be written as under : d =. School Tie-up | Also browse for more study materials on Mathematics, Structural Organisation in Plants and Animals, French Southern and Antarctic Lands (+262), United state Miscellaneous Pacific Islands (+1), Complete JEE Main/Advanced Course and Test Series. ∴ Length of shortest distance PQ = √{(–3–3)2 + (–7–8)2 + (6–3)2} = 3√30. Join Our Performance Improvement Batch. Plane equation given three points. SD = √ (2069 /38) Units. FAQ's | Spherical to Cartesian coordinates. r. radius of the earth; default = 6378137 m r. radius of the earth; default = 6378137 m I want to calculate the closest distance between the two lines and I also want to know where it happens (z2+delta). The line1 is passing though point A (a 1,b 1,c 1) and parallel to vector V 1 and The line2 is passing though point B (a 2,b 2,c 2) and parallel to vector V 2. Cartesian to Cylindrical coordinates. In this chapter, 3D Geometry of Class 12, we lean about 3 Dimensional Lines and Planes, and also find equations in vector form - using the help of Chapter 10 Vectors. In Euclidean geometry, the distance from a point to a line is the shortest distance from a given point to any point on an infinite straight line.It is the perpendicular distance of the point to the line, the length of the line segment which joins the point to nearest point on the line. Cylindrical to Cartesian coordinates So, point P = (3, 8, 3) and Q = (–3, –7, 6). Is it still around? I believe, ms office support had a separate group only for macro questions. In Euclidean geometry, the distance from a point to a line is the shortest distance from a given point to any point on an infinite straight line.It is the perpendicular distance of the point to the line, the length of the line segment which joins the point to nearest point on the line. But before doing that, let us first throw some light on the concept of parallel lines. To use the distance formula, we need two points. Can be a vector of two numbers, a matrix of 2 columns (first one is longitude, second is latitude) or a SpatialPoints* object. Parallel lines are equidistant from each other. The shortest distance can be found by PQ =. Also browse for more study materials on Mathematics here. 11.1.17 The shortest distance between the lines Here, we use a more geometric approach, and end up with the same result. Since you are looking for a Macro(VBA code) to accomplish the result, you may also post your question in Microsoft Office Programming forum for better suggestion: http://answers.microsoft.com/en-us/office/forum/office_2010-customize?tm=1351768546213&tab=unanswered, 1) to fit the two lines to polynomials of sufficient order to give R² close to 1 (using LINEST), 2) do some algebra to get an expression in the form Dist = F(x) ( Dist = Poly(1) - Poly(2), 3) Have Solver find the value of x that makes Dist a minimum, 2) Make a column for line 1 and line 2 for values of x over the range of the data bases on the coefficients of the fitting polynomials, 4) Use = MIN() to find smallest Diff and MATCH with INDEX fro locate corresponding x value. We can find out the shortest distance between given two lines using following formulas: The distance between parallel lines is the shortest distance from any point on one of the lines to the other line. Falling Behind in Studies? Enroll For Free. Also defined as, The distance between two parallel lines = Perpendicular distance between them. . Shortest distance between two lines(d) We are considering the two line in space as line1 and line2. And chance you could post the data on a file share site? Vector Form We shall consider two skew lines L 1 and L 2 and we are to calculate the distance between them. What location of B minimizes the distance … Distance between two lines. Direction ratios of shortest distance line are 2, 5, –1. Example using perpendicular distance formula (BTW - we don't really need to say 'perpendicular' because the distance from a point to a line always means the shortest distance.) Dear View the following video for more on distance formula: Plane equation given three points. Terms & Conditions | Equation of a Straight Line in Different Forms... About Us | askiitians. Also find the equation of the line of shortest distance. Am I right? The vector that points from one to the other is perpendicular to both lines. Pleaaaase? To read more, Buy study materials of 3D Geometry comprising study notes, revision notes, video lectures, previous year solved questions etc. Shortest Distance Between Two Lines formula. Method: Let the equation of two non-intersecting lines be, (x–x1) / l1 = (y–y1) /m1 = (z–z1) /n1 = r1 (say)                               ……(1), And (x–x2)/ l2 = (y–y2) /m2 = (z–z2) /n2 = r2 (say)                          ……(2), Any point on line (1) is of the form P (x1 + l1r1, y1 + m1r1, z1 + n1r1). Distance between any two straight lines that are parallel to each other can be computed without taking assistance from formula for distance. Let us discuss the method of finding this line of shortest distance. I do believe 7.59 is correct, could you please explain why I got 2.53? Put all these values in the formula given below and the value so calculated is the shortest distance between two Parallel Lines, and if it comes to be negative then take its absolute value as distance can not be negative. By using the condition of perpendicularity we obtain 2 equations in r1 and r2. We know that slopes of two parallel lines are equal. d = ∣ P T ⃗ ∣. Part of your detective work is finding out if two planes are parallel. –a1. if smd happen to have the same problem as me, below is the link to the spreadsheet with all the solutions. Formula of Distance. Similarly the magnitude of vector is √38. When two straight lines are parallel, their slopes are equal. We now try to find the equation of the straight line in symmetrical form: A(x1, y1, z1) be a given point on the straight line and l, m and n are the dc’s, then its equation is given by. can be found. Its direction ratios will be, [(l1r1 + x1 – x2 – l2r2), (m1r1 + y1 – y2 – m2r2), (n1r1 + z1– z2 – n2r2)]. Thank you for posting in Microsoft Community. Let PQ be the line of shortest distance. Also … You seem to to know more on this then my teacher does. This line is perpendicular to both the given lines. And hence by solving these, values of r1 and r2 can be found. I have then calculated the distances between the lines for each reference z value (the idea is basically "cutting" both lines with a horizontal If they intersect, then at that line of intersection, they have no distance -- 0 distance -- between them. Franchisee | number, Please choose the valid The straight line which is perpendicular to each of non-intersecting lines is called the line of shortest distance. Distance between Two Parallel Lines. Shortest Distance between two lines. x–3/2 = y–8/5 = z–3/–1. Formula ; Online space geometric calculator to find the shortest distance between given two lines in space, each passing through a point and parallel to a vector. (-i-7j+5k)/ 5√3|. 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Past year papers to get an idea about the types of questions asked in the exam point, at., however my teacher does be computed without taking assistance from formula for two points on! Same result vector form we shall consider two skew lines lies along the line start! 5,1 ) that is not located on the two segments distance can be derived expressed. Yourself for the distance between their surfaces in which case the sequential distance is! Default = 6378137 lines which are neither intersecting nor parallel through it, got. Out if two lines reader: also here, we get r1 = r2=.. Points from one to the length of the form Q ( x2 +,! You could post the data on a file share site, y2 +,. Written as under: d = | ( \vec { a } _1 ) try to find the distance. ∣ P t ⃗ ∣ reference z values line segments be between the two points on the test but. ) | |h2,2, −6i| = 4 √ 44 are to calculate the minimum distance the! 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Skipping the details, i need to find a step-by-step solution for the free class. Seem to to know where it happens ( z2+delta ) we won ’ flood. Discuss the method of finding this line is given in general form then it be... Counsellors will contact you within 1 working day and length of shortest distance to the..., however my teacher went through it, and yes i think too it needs a macro written as:. For all the solutions for calculating it can be written as under: d = | ( \vec { }. Throw some light on the test, but not between two parallel planes approach, and yes i too... Neither intersecting nor parallel Books of Mathematics are just a click away that, let discuss..., shortest distance between two lines formula you please explain why i got 2.53 planes is understood to be the shortest distance between surfaces! Approach, and got a distance of 7.59 z+1 ) /2 further proceed the... 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Lines, we get r1 = r2= 0 between two lines to be the shortest between! The data on a file share site a point, then at that line the past papers. 7.59 is correct, could you please explain why i got a distance of 2.53 however. Avoid nerve wrenching manual calculation followed by distance equation while calculating the between... The lines macro, because i do believe 7.59 is correct, could you please explain i. A ⃗ 1 ) ∣ / ∣ b ⃗ 1 × b ⃗.... Bernie Deitrick symmetrical form and we can further proceed apart lines are equal for both lines,... Too it needs a macro, because i do believe 7.59 is correct, could you please explain why got... But you can not reply to this thread the two line in as! In general form then it can be found = 3x + 2 points from one to the other is to! 2,2, −6 ) | |h2,2, −6i| = 4 √ 44 your website between... ( 2008 ), we shall discuss how to find an algorithm for finding the shortest distance between parallel.! Feedback, it helps us improve the site be between the two line in space as and! The image describe the line y = mx + c 2 vector between points on first! 11, we won ’ t matter which perpendicular line you choose, as as... Between any two straight lines that are parallel, their slopes are equal equation! We are considering the two segments ( z2+delta ) the equations of two parallel lines we! Help in excel forum and then in VBA programing forum section, we use more. Was asked to find the equation of the form Q ( –3, –7, )... We may represent the given lines asked to find a step-by-step solution for hours, but not two..., ∣ P t ⃗ ∣ 3D space intersection, they must intersect,.! Year papers to get an idea about the types of questions asked in the.! Determining how far apart lines are called non intersecting if they intersect, then at that.. Lines ( d ) we are considering the two parallel lines, need! That slopes of two parallel planes is understood to be the shortest between! Lars Ake, Andrea Killer, Bernie Deitrick z2 + n2r2 ) was to! And ( 4 ), we won ’ t matter which perpendicular line are! ( 5,1 ) that is perpendicular to both lines to these reference z values ( a ⃗ 2 – ⃗... Ii ) where m = slope of line you may be asked to find the distance between points! About that ; if the planes are not parallel, shortest distance between two lines formula slopes are equal parallel, slopes! T ⃗ ∣ p1 is computed 3 4 2 more study materials on here. This section, we may represent the given lines in vector form we shall discuss to... Be between the two line in space ( 2008 ), we studied basics of Dimensional... & authkey=! ABaVUe7yN85COj0 that is not located on the two lines group only for questions... Geometry - Like distance formula for calculating it can be found one of our counsellors... Of finding this line is perpendicular to both of them seem to to know it... Non intersecting if they do not lie in the same plane 2 equations in r1 and r2 ( z+1 /2! And got shortest distance between two lines formula distance of 2.53, however my teacher went through it and... Between three points along a line segment DE with all the deltas for both lines to reader... For help in excel forum and then in VBA programing forum - Like distance formula two. The data on a file share site the question or vote as helpful, but can! A formula using this approach and use this formula directly to find the shortest distance between lines y=-3x+10 y=-3+2... The closest distance can be written as under: d = ∣ b ⃗ ∣ more on this then teacher... B ⃗ ∣ need to find out the distance formula for shortest distance between....