If with reference to the right handed system of mutually perpendicular unit vectors `hati, hatj, hatk`, `vec alpha = 3hati - hatj, vec beta = 2hati + hatj - 3hatk`, then express `vec beta` in the form `vec beta = vec beta_1 + vec beta_2` where `vec beta_1` is parallel to `vec alpha` and `vec beta_2` is perpendicular to `vec alpha`.

Answer

`vec(beta)=(3/2hati-1/2hatj)+(3/2hati+3/2hatj-3hatk)`