This vector question has three parts, and I've done the first two,

finding the point of intersection and acute angle between them.

It's the third bit I don't understand.

$\displaystyle L_1\!:\;\;2i-j+3k + s(j-k)$

iii) The foot of the perpendicular from the point $\displaystyle A$

with position vector: $\displaystyle -2i+7j+3k$ to line $\displaystyle L_1$ is $\displaystyle P.$

Find the position vector of $\displaystyle P.$ Code:

A
*
\
\
\ L1
\ *
\ *
*
* P
*

$\displaystyle AP$ is drawn perpendicular to $\displaystyle L_1$

We are asked to locate point $\displaystyle P.$