If `veca` makes equal angles with `hati, hatj` and `hatk` and has magnitude 3, prove that the angle between `veca` and each of `hati, hatj` and `hatk` is `cos^(-)(1/sqrt3)`.

Explanation

Given `alpha = beta = gamma`
therefore `cos^2alpha+cos^2beta+cos^2gamma = 1`
`implies 3cos^2alpha = 1 implies cosalpha = +-1/sqrt3`
therefore `alpha = cos^(-1) (+-1/sqrt3) = beta = gamma`