# Question on skew lines

• Dec 13th 2010, 02:37 PM
s3a
Question on skew lines
The question is attached (#1, parts a and b). I have no idea how to do part b and as for part a. I don't remember what I did but when I try to think about the problem: I see that to find that the lines do not intersect I need to find that there is an inconsistence between the s[7,-1,-2] and t[1,1,2] slopes. (Is that what they're called?) Also, to find that they're not parallel I need some matrix to have only nonzero rows but I am confused as to which matrix I look at for the parallel one. Is it the same as the one where I looked for the inconsistence?

If I'm unclear, please tell me.

Any help would be GREATLY appreciated!
• Dec 13th 2010, 02:52 PM
Plato
If you really want help then you will type out the question in a readable format.
• Dec 13th 2010, 04:26 PM
s3a
• Dec 13th 2010, 04:30 PM
Plato
Quote:

Originally Posted by s3a

Well good luck with that non responsive reply.
• Dec 13th 2010, 04:34 PM
s3a
I still don't get the problem, are you not able to see the image or something? I retyped it though like you asked:

"Consider the lines l1: [-5,4,3] + s[7,-1,-2] and l2: [4,-1,8] + t[1,1,2].
(a) Show that l1 and l2 are skew lines.
(b) What is the distance between l1 and l2?"
• Dec 14th 2010, 04:00 AM
Plato
Given two skew lines: $\ell _1 :P + tD\;\& \,\ell _2 :Q + tE$
then the distance between them is
$d\left( {\ell _1 ,\ell _2 } \right) = \left[ {\dfrac{{\left| {\overrightarrow {PQ} \cdot \left( {D \times E} \right)} \right|}}
{{\left\| {D \times E} \right\|}}} \right]$
.

In this question $D = \left\langle {7, - 1, - 2} \right\rangle \;\& \,E = \left\langle {1,1,2} \right\rangle$