Determine the least value that the area of the triangle OAP can take. O is the origin, A is known and P is an unknown point on a line

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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.