I have two lines
$$ l_1: \begin{cases} x=-14-4t\\ y=5+t\\ z=t \end{cases} $$
$$ l_2: \begin{cases} x=t\\ y=2t\\ z=2t \end{cases} $$
I have a known point A on $l_2$,
$$ A=(1,2,2) $$
and an unknown point P on $l_1$, which I want to use to minimize the area of the triangle OAP, where O is the origin. How do I do this? I'm having troubles visualizing this as I tried doing it by finding the shortest distance between the lines to use as the length of one of the sides in the triangle and use the formula for triangles $\frac{b\cdot h}{2}$, but I got the wrong answer. So it must be something else.