Question

find the distance between 2 skew lines:
L1: r=(2,3,1) +t(1,2,1)
L2: x=z, y=1

Answer 1

im thinking if we cross the 2 direction vector of the line, we can define a plane that is parallel to both lines

Answer 2

since we have a clearly defined point in L1, we can place this plan such that L1 is encased with in it, then my thought wanders and i have to narrow it down again.

of course, if there was a formula that i could remember to make this simpler, that oul dbe easier :)

Answer 3

L2 can be constructed from points like: (0,1,0) (1,1,1) (2,1,2)

this is a 45degree line to the xy plane, parallel to the zx plane, and running thru the y=1 plane

Answer 4

I just typed up a much too long answer.

Answer 5

L1:
x = 2+1t
y = 3+2t
z = 1+1t

L2:
x = 0 + 1t
y = 1 + 0t
z = 0 + 1t


L1xL2:
x 1 1 : x= 2
y 2 0 : -y= 0
z 1 1 : z= -2

a plane that contains L1 and is parallel to L2 is:

2(x-2)-2(z-1) = 0
2x -4 -2z+2 = 0
2x - 2z = 2

x-z = 2

hmmm, a plane that contains L2 and is parallel to L1 is:

2(x-0)-2(z-0) = 0
2x-2z = 0

x-z = 0

what to do with that ....

Answer 6

at least I was on the right track :) thnx phi

Answer 7

i was going to try to determine the distance between the "linear" aspects of the equations

Answer 8

don't stop on my account.