There are two lines in $ \Bbb R^3 $ given in parametric form: $$ l_1: \left\{ \begin{aligned} x &= x_1 +a_1t\\ y &= y_1 +b_1t \\ z &= z_1 +c_1t \\ \end{aligned} \right. $$ $$ l_2: \left\{ \begin{aligned} x &= x_2 +a_2s \\ y &= y_2 +b_2s \\ z &= z_2 +c_2s \\ \end{aligned} \right. $$
What's the simplest method (or formula) for finding (the shortest) distance beteen them?
example I'm doing:
$
l_1:
\left\{
\begin{aligned}
x &= 0 \\
y &= -1 - 2t \\
z &= -2t \\
\end{aligned}
\right.
$
$ l_2: \left\{ \begin{aligned} x &= 3s \\ y &= 1 - s \\ z &= 2 + 4s \\ \end{aligned} \right. $
Hint: Find a vector $\mathbf A$ perpendicular to both lines and then find the projection onto $\mathbf A$ of any vector joining $\ell_1$ and $\ell_2$. Pictures help.