What is Shortest distance: Definition and 71 Discussions
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.
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...
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!
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...
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...
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
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...
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 (...
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
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...
[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 +...
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...
... 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)...
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...
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...
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..
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?
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
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 *...