How to project vector onto a plane but not along plane normal? In 3d space, is there any way to project a vector onto a plane, but along the UP direction (0,1,0) instead of the plane normal? If so, how do I do that and what is it called?

A picture would help, but this is what I think you are asking. Given the plane $ax+by+cz = d$ and the point $(p,q,r)$, you want to move the point in the direction $(0,1,0)$  until it meets the plane.
Well that move will change only the value of $q$, To find the new value, solve
$$
ap + b? + cr = d
$$
for the value of $?$.
There will be no solution if $(0,1,0)$ is parallel to the plane (unless the point is in the plane to begin with).
In more generality, you are asking for the intersection of a line (through a given point in a given direction) with a plane.
