Show that if a vector a forms angles α, β, and γ with the coordinate axes, then cos2 α + cos2 β + cos2 γ = 1. (Hint: Show that the components of the vector are ∥a∥ cos α, ∥a∥ cos β, and ∥a∥ cos γ.) The cosines of α, β, and γ are called the direction cosines of a.
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