What is a formula to get a vector perpendicular to another vector?

Question

What is a formula to get a three dimensional vector B lying on the plane perpendicular to a vector A?

That is, given a vector A, what is a formula f(angle,modulus) w

Answer 1

Calculate the cross product AxC with another vector C which is not collinear with A.

There are many possible directions in the plane perpendicular to A. If you don't really care, which one to pick, just create an arbitrary vector C not collinear with A:

if (A2 != 0 || A3 != 0)
    C = (1, 0, 0);
else
    C = (0, 1, 0);
B = A x C;