The shortest distance between the lines x+1=2y=-12z and x=y+2=6z-6 is:

Question

The shortest distance between the lines $x+1=2y=-12z$ and $x=y+2=6z-6$ is:

Accepted Answer

$L_{1}: \frac{x+1}{1}=\frac{y}{\frac{1}{2}}=\frac{z}{\frac{-1}{12}}$

$$
\begin{aligned}
& L_{2}: \frac{x}{1}=\frac{y+2}{1}=\frac{z-1}{\frac{1}{6}} \\
& \text { S.D }=\left|\frac{(-\hat{i}+2 \hat{j}-\hat{k}) \cdot(2 \hat{i}-3 \hat{j}+6 \hat{k})}{7}\right| \\
& =\left|\frac{-2-6-6}{7}\right|=2 \text { units }
\end{aligned}
$$

Solutions · 1