How to tell if a point is located on a plane?

Question

$P(-3,4,-5)$ and the plane is $(1,-5,6)+s(2,1,3)+t(1,7,1)$

How exactly do I go about with this? I believe that I'm supposed to put the plane in parametric form (see below), then substitute the $x,y,z$ of the point into it? Where do I go from there? Any help is greatly appreciated. $$\begin{align*} x&=1+2s+t\\ y&=-5+s+7t\\ z&=6+3s+t \end{align*}$$

Answer 1

you must solve the system $$-3=1+2s+t$$ $$4=-5+s+7t$$ $$-5=6+3s+t$$ for $s$ and $t$

Answer 2

A quick way is to work out the cross product of the coplanar vectors $(2,1,3)$ and $(1,7,1)$ and see if this is perpendicular to the vector joining $(-3,4,-5)$ and $(1,-5,6)$ using dot product.

If they are perpendicular then this point lies on the plane.