Homepage › Solution manuals › Gilbert Strang › Introduction to Linear Algebra › Exercise 1.2.17
cos α = 1∕2,cos β = 0,cos γ = −1∕2. For any vector v = (v1,v2,v3) the cosines with (1,0,0) and (0,0,1) are cos 2α + cos 2β + cos 2γ = (v12 + v22 + v32) ∕∥v∥2 = 1