Perpendicular Vector3 to a given Vector3

Question

How can I find a Vector3 which is perpendicular to given Vector3? Maybe rotate the Vector3 90 degrees or something, is there a vector3 function that can do that?

This image illustrates what I am trying to accomplish:

Answer 1

The thing is, there is an infinite amount of vectors perpendicular to any given vector in 3D space. You need a second vector not parallel to the first one to find a vector perpendicular to them both, i.e. their cross product, since this way a plane is defined, which may have only one perpendicular line.

In Unity, cross product is computed by the static method Vector3.Cross().

Answer 2

To answer your original question: how to compute a vector perpendicular to another?

Let's call your vector p and the vector we're looking for that is perpendicular to it q. Note that there are an infinite number of vectors q but we're just going to find one.

For perpendicular vectors the dot product is always 0 so we find the equation p · q = 0 which we can write as p.x * q.x + p.y * q.y + p.z * q.z = 0. Now we're going to assign arbitrary values to q.x and q.y in order to fix one solution, let's pick q.x = 1 and q.y = 1. Then we're left with p.x + p.y + p.z * q.z = 0. Solving for q.z gives us q.z = -(p.x + p.y) / p.z.

In conclusion: the vector q = (1, 1, -(p.x + p.y) / p.z) is perpendicular to p.