I have three non-parallel vectors (whose components are known), v0, v1, v2 and I'd like to find a fourth unit vector, v3, given only the angles between: psi, angle between v0 and v3 theta, angle between v1 and v3 phi, angle between v2 and v3 I know that they are related by the dot product: v0 . v3 = |v0||v3| cos(psi) v1 . v3 = |v1||v3| cos(theta) v2 . v3 = |v2||v3| cos(phi) this give me a system of equations to solve, however, I have a term on the right side |v3|, expands into sqrt(a^2+b^2+c^2) - so its not quite linear. If I have the constraint that I want to find a UNIT vector v3, ie. |v3|=1, then can i just set sqrt(a^2+b^2+c^2)=1, to make it a linear system? Also - is there an easier way to solve this?