If `vec(a)` makes equal angles with `hat(i), hat(j)` and `hat(k)` has magnitude 3, prove that the angle between `vec(a)` and each of `hat(i), hat(j)` and `hat(k)` is `cos^(-1)""(1)/((sqrt(3)))`.

Answer

`a = pm 3((1)/(sqrt(3))hat(i) + (1)/(sqrt(3))hat(j) + (1)/(sqrt(3))hat(k))`