A vector makes angles α, β, γ with +x,+y,+z. If cosα=1/2, cosβ=1/2 and its z-component is positive, find cosγ.
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Question

A vector makes angles α, β, γ with +x,+y,+z. If cosα=1/2, cosβ=1/2 and its z-component is positive, find cosγ.

G1 Physics · Accepted Answer

Direction cosines satisfy l²+m²+n²=1. Thus n²=1−1/4−1/4=1/2. Positive z gives n=1/√2.