# Calculate perpendicular vector that sits on plane

I was hoping someone could help me out with some vector math

Say I had 3 3D points, A, B, C, which form a plane called ABC. I would like to move point B by 10 units, along a vector that is perpendicular to the vector AC, and sits on the plane ABC.

How do I calculate the vector that is perpendicular to AC, and sits on the plane ABC?

Vector you need to find is b Question gives us two conditions that it lies in plane ABC and is perpendicular to AC Let's assume that equation of ABC is $$ax+by+cz=d$$
$$(a,b,c) \cdot b = 0$$
$$b \cdot AC = 0$$
$$(a,b,c)*AC$$