Find the projection of the point on the plane I want to find the projection of the point $M(10,-12,12)$ on the plane $2x-3y+4z-17=0$. The normal of the plane is $N(2,-3,4)$.
Do I need to use Gram–Schmidt process? If yes, is this the right formula?
$$\frac{N\cdot M}{|N\cdot N|} \cdot  N$$
What will the result be, vector or scalar?
Thanks!

You can use calculus to minimize the distance (easier: the square of the distance) of M from the generic point of the plane.
Use the equation of the plane to drop a variable, obtaining a function of two independent variables: compute the partial derivatives and find the stationary point. That's all.
