Posted by J on .
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.

Calculus 
Steve,
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 
Calculus 
J,
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:
L1: [x,y,z]=[1,1,0]+s[3,4,2]
L2: [x,y,z]=[5,9,4]+t[2,3,1]
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:
9x2y+12z

229^1/2
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 ....