1. The problem statement, all variables and given/known data I have an a-b coordinate system which is skewed with an angle = 60 deg. I also have a particle position defined by vector V1 (a1, b1, 0) which follows the coordinate system. The problem I have is that I need to get V2 (a2, b1, 0) which is perpendicular to V1. 2. Relevant equations 3. The attempt at a solution I tried a normal cross product to generate V2 V2 = V1 (a1, b1, 0) x Z (0, 0, 1) = |b1| (a^hat) - |a1| (b^hat) = V2 (b1, -a1, 0) which works sometimes but not at all points in space. I was thinking this way is only applicable for orthogonal coordinate system.