8. Let α, β, γ be the angles made by a vector u ∈ R 3 with positive x, y, z−axis respectively. Then, the numbers l = cos α, m = cos β, n = cos γ are called the direction cosines of u.
(a) Find the formulas for the direction cosines: l, m, n of the vector u = hu1, u2, u3i.
(b) Prove that l 2 + m2 + n 2 = 1.
(c) Find the direction cosines l, m, n of the vector u = h1, −1, 1i.
