Finding the normal from one 3d vector/line to any point on another 3d vector/line

Question

Say I have two 3d vectors, v1 and v2 (you can consider them both lines if you like). I'm trying to figure out a normal for v1 so that it intersects along any point of v2.

I keep drawing blanks on this one. It's easy enough to find a vector that points from v1 to v2 (just do v2 - v1), but that result isn't always perpendicular to v1.

How would you go about making that result perpendicular to v1?

Answer 1

You can use scalar projection, i.e. the dot product, to do that.

You want to project v2 onto v1, so normalize v1 to length 1, then take the dot product: float projection = dot(v2, normalize(v1));

This tells you how far you have to go in the direction of v1 until you are perpendicular to the end of v2, so float scalar = projection / length(v1); tells you where on v1 that point is.

so scalar * v1 gets you to that point, and v2 - scalar*v1 would be the perpendicular vector from that point on v1 to v2.