Prove that sum of the cosines squared of the angles between a vector and the x, y, and z axes equals 1. Prove using either geometry or vector algebra.
The Attempt at a Solution
I started by trying to pull out the angles with
(Edit: This is no longer valid)
This doesn't make sense to me since I know that the maximum sum of the angles can only be around 180 degrees (I think). So I thought maybe the geometric approach would have something to do with triangles. But I don't know how to show that analytically.
(Edit: Still clueless)
I'm also lost on how to start with the vector algebra. I'm looking over the identities of vectors now but to no avail.