Shortest distance Definition and 72 Threads

In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of the segment.

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  1. I

    Shortest distance between two skew lines

    Homework Statement What is the shortest distance between these two lines? L1:(x,y,z)=(4,−2,−2)+t(1,1,−3) L2: The line through the points (−2,−2,0) and (−4,−5,0)Homework Equations distance formulaThe Attempt at a Solution I thought I was on the right track but apparently not. For L1, I took 2...
  2. I

    Shortest Point on Cylinder Vertices

    What will be the shortest point on the opposite "vertices" of a cylinder?
  3. D

    Shortest distance between two points (one unknown?)

    Homework Statement Find an equation of the line, say y=mx+b, which passes through the point (6,−2) and is perpendicular to the line −2x+4y=0 y= What is the shortest distance from the point (6,−2) to the line −2x+4y=0? Homework Equations ? The Attempt at a Solution So I...
  4. F

    Shortest distance between two lines (vector algebra)

    Homework Statement line l1 : x=2 y= -1 + p z= 2p line l2 : x=-1 + t y=1-3t z=1-2t Find the shortest (exact) distance between l1 and l2. Homework Equations That's what I am looking for! The Attempt at a Solution Thanks!
  5. G

    Shortest distance between two lines

    Hi guys this problem should be simple enough but I just can't get the correct answer. Well the question is: Show that the shortest distance between the line (l_1) with equation \frac{x+4}{3} = \frac{y-3}{2} = \frac{z+6}{5} and the line (l_2) with equations i. x -2y -z =0 ii. x...
  6. A

    The shortest distance along cone

    Homework Statement Obtain an integral formula for the length of a curve p(theta) along a right cone. use spherical coordinates p and theta. Answer: L = integral from -pi/2 to pi/2 of sqrt(p'^2 + p^2/R^2)d(theta) Homework Equations p is distance from origin altitude a, radius 1...
  7. R

    Shortest distance between lines .

    shortest distance between lines... how to find the shortest distance and the equation between the lines (x-6)/3=(y-7)/-1=(z-4)/1 & (x)/-3=(y+9)/2=(z-2)/4 ... pls help by solving it
  8. A

    Shortest Distance Homework: Find Origin to Curve x^2+2xy+y^2=150

    Homework Statement Find the shortest distance from the origin to the curve x^2+2xy+y^2=150. Homework Equations \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} 3. The problem I'm occurring I'm not sure how to start is thus can't attempt it. I would have used the...
  9. V

    How to Calculate the Shortest Distance Between Atoms in a BCC Structure?

    Homework Statement Barium crystallizes in a body centered cubic structure in which the cell edge length is 0.5025 nm. Calculate the shortest distance between neighboring atoms in the crystal. Homework Equations Avagodro's number The Attempt at a Solution 0.5025 x 10^-7 cm (...
  10. N

    How Is the Shortest Distance Between Two Vectors Determined?

    Say you have two vectors: a and b. Is the shortest distance between these two vectors when a line perpendicular to a meets vector b, or when a line perpendicular to vector b meets vector a? Thanks
  11. G

    Is the Shortest Distance Between P and F(x) Along a Perpendicular Line?

    This is sort of a simple question. If there is a point P near a function F(x), then, so long as F(x) is continuous, the shortest distance between P and F(x) would be along a line connecting P and F(x), in which it is perpendicular to the tangent of F(x) at the point of intersection. Is...
  12. J

    Solve Shortest Distance to Origin on Quadric Surface

    [SOLVED] shortest distance Homework Statement Find the shortest distance to the origin given the quadric surface x^2 + y^2 - 2zx = 4Homework Equations The Attempt at a Solution F = x^2 + y^2 + z^2 g = x^2 + y^2 - 2zx = 4 Well I initially substituted y^2 = 4 + 2zx - x^2 into F F = 4 + 2zx +...
  13. R

    Find Shortest Distance of y=x^2 from (4,0)

    shortest distance?? Homework Statement find the shortest distance of y=x^2 from (4,0) Homework Equations The Attempt at a Solution if y=x^2, then y'=2x where x=4 the slope is 8 the solution is y=8(x-4) if that is the tangent line \, the normal line would be...
  14. N

    Shortest distance from a point to a line

    ... on a sphere. Ok, so this isn't really a homework question (I haven't done homework in years), but rather is a problem I've been trying to figure out for the last few hours for a programming issue I have run into. So if this is the wrong forum, feel free to move it (and I apologize)...
  15. K

    Is the Proof for the Nearest Point in a Cone Valid?

    I encountered a problem in a book with a proof given. But I am a bit skeptic about it. I hope someone can help shed some light. Let \{g_{i}\} be a set of vectors and imagine a cone defined as K = \left\{v \,\bigg|\, v =-\sum_{i}\lambda_{i}g_{i}, \textup{ where }\lambda_{i}\geq 0 \ , \forall i...
  16. H

    Does the shortest distance exists?

    Is there a shortest possible distance besides zero? Or there's no limitation at all?
  17. G

    Optimizing Two Cyclists' Speeds at a Perpendicular Intersection

    Firstly I apologise if my problem here seems a bit daft but I have got nobody other than myself or you guys to tell me if I'm doing things correctly or not. The question: Two cyclists are riding one along each of two perpendicular roads that meet at A. At one instance both cyclists are 500m...
  18. F

    Find the shortest distance between the two skew lines

    Find the shortest distance between the two skew lines L(1) and L(2) with equations r = (1, 2, 2) + s (4, 3, 2) and r = (1, 0, -3) + t (4, -6, -1) How to do this? Help needed..
  19. S

    Shortest distance between two points. Line?

    I would like to see the proof that the shortest distance between two points is a line. I found a proof online http://www.instant-analysis.com/Principles/straightline.htm but i can't quite follow it. Does anyone know of a simple proof of this fact?
  20. M

    Shortest Distance btw Point & Hyperbola

    hi, pls anyone, how would i find the shortest distance btw a point (x,y) and a hyperbola , given the equation of the hyperbola?? :rolleyes:
  21. Y

    Find the shortest distance between 2 non-paralle lines (skew lines) in 3-space

    explain how you go about finding the shortest distance between 2 non-parallel lines (i.e. skew lines). for example: x=3-2t, y=1-4t, z = t and (x+2)/3=y+1=(z+1)/-2
  22. L

    Shortest distance from point to Catmull-Rom spline

    If I have a point P, how do I project it onto a Catmull-Rom spline (ie. get the point on the spline closest to P)? This is how I calculate the spline, t goes from 0 to 1 (C++): float t2 = t * t; float t3 = t2 * t; out.x = 0.5f * ( ( 2.0f * p1.x ) + ( -p0.x + p2.x ) * t + ( 2.0f *...
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