# Math Help - Distance Between Two Lines?

1. ## Distance Between Two Lines?

Let P=(–5,–2,4) , Q=(–4,0,5) , R=(–2,–5,6) and S=(–5,1,6) . Let L1 be the line passing through P and Q, and let L2 be the line passing through R and S.

What is the distance between L1 and L2?

2. $
L_1=P+
\begin{bmatrix}
1 \\ 2 \\ 1
\end{bmatrix}
L_2=R+
\begin{bmatrix}
-3 \\ 6 \\ 0
\end{bmatrix}
$

These lines are not parallel. Therefore we compute the distance as follows:
$
D=\frac{|\vec{RP}\cdot(v_1\times v_2)|}{||v_1\times v_2||}
$

where $v_1,v_2$ are the direction vectors for the two lines.Thus the distance is calculated:
$
D=\frac{15}{\sqrt{117}}
$

3. I did that, but it says that I'm incorrect.

4. Ah nevermind, the magnitude of the normal is sqrt189, not 117. Thanks though, you were of great help!