Computing two vectors that are perpendicular to third vector in 3D

Question

What is the best (fastest) way to compute two vectors that are perpendicular to the third vector(X) and also perpendicular to each other?

This is ho

Answer 1

There is a method to find a good HELPER (really - it is ready to be your y_axis).

Let's X = (ax, ay, az). Choose 2 elements with bigger magnitude, exchange them, and negate one of them. Set to zero third element (with the least magnitude). This vector is perpendicular to X.

Example:

if (ax <= ay) and (ax <= az) then HELPER = (0, -az, ay) (or (0, az, -ay))

X*HELPER = 0*0 - ay*az + az*ay = 0

if (ay <= ax) and (ay <= az) then HELPER = (az, 0, -ay)