Given vectors a, b, and p, I am trying to find unit vector u, such that u is in the plane spanned by a and p and is orthogonal to b.
Assume all vectors are unit vectors
I can form 3 equations:
u.b = 0 (orthogonal to b)
u.(a x p) = 0 (in plane spanned by a and p)
|u| = 1 (unit vector)
and so solve for the components of u, but i was wondering if there anything more elegant?
Best Answer
u is of the form $\lambda \textbf{a} + \mu \textbf{p}$, and $\textbf{u.b} = 0$. So $\lambda \textbf{a.b} + \mu \textbf{p.b} = 0$. This, together with the requirement that u is a unit vector, is enough to determine $\lambda$ and $\mu$.