# Thread: Identifying points from lines

1. ## Identifying points from lines

Hi,

I hope someone can help.

I know that the direction vector for line 1 is (2,1,-1) and for line 2 is (3,2,-3).

Not sure where to go from here.

- otownsend

2. ## Re: Identifying points from lines

Originally Posted by otownsend

I know that the direction vector for line 1 is (2,1,-1) and for line 2 is (3,2,-3).
I don't know what the author of the questions wants you to do.
But lines $L_1~\&~L_2$ are skew. It is well known that the is a unique perpendicular to each of two skew lines.
Suppose that $L_1: A+tD~\&~L_2: B+sE$
Using the hint, let $P\in L_1~\&~Q\in L_2$ So $\overrightarrow {PQ}$ will perpendicular to both $D~\&~E$.
Moreover, $\overrightarrow {PQ}$ will parallel to $D\times E$.

This is quite a tedious task. I don't envy you trying to juggle these ordinates.

3. ## Re: Identifying points from lines

$\overrightarrow {PQ}$ parallel to $D\times E$

means

$\overrightarrow {PQ} = \lambda D\times E$ for some real number $\lambda$

that's a vector equation so we have three equations in three unknowns $t,s,\lambda$