posted by J .
Find the distance between the lines [x,y,z] = [-1,1,0] + s[3,4,-2] and [x,y,z] = [5,9,-4] + t[2,3,1]. Interpret the result.
As I recall, if you have two lines
L1: p1 + v1*t
L2: p2 + v2*t
the distance can be obtained by projecting the unit normal between the lines onto the line joining the two points:
v1 × v2 / |v1 × v2| • (p1 - p2)
For a brief example and discussion, see
physicsforums . com / showthread.php?t=276253
for this question, do i have to solve it? it just says interpret the results, does that mean only explain?
im trying to solve it right now. i have:
First, cross product of the two directional vectors from both lines:
[3,4,-2] x [2,3,1] =
That's all I have so far :/
I don't know what to do next because in the example shown on the forum, I don't know how they got the answer [from the forum: (-2,3,-2) x (-2,-3,-1) = (-9,-2, 12)] I know 3 x (-3) is -9 but I don't understand where the -2 and +12 came from since (-2)(-2) = +4 and (-2)(-1)= +2.
Also on the forum there is:
And its unit vector is:
I don't know how they got this answer either. They mentioned at the end of it they may not be right so I don't know ....