If cos α, cos β, cos γ are the direction cosines of vector $\vec{a}$, then the value of cos 2α + cos 2β + cos 2γ is equal to :
Answer & explanation
Correct answer: option 4
cos α, cos β, cos γ → direction ratios of $\vec{a}$ so
cos2α + cos2β + cos2γ = 1 ........(1)
so cos 2α + cos 2β + cos 2γ
as cos 2x = 2cos2x - 1
= 2cos2α - 1 + cos2β - 1 + 2cos2γ - 1
= 2(cos2α + cos2β + cos2γ) - 3
= 2 × 1 - 3
= -1