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If a vector has direction angles α = π/4 and β = π/3, find the third direction angle γ

Craig Stewart

in Mathematics

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Jennifer Patterson on September 16, 2018

For a vector:cos^2(α) + cos^2(β) + cos^2(γ) = 1from the givens:α = π/4, so cos(α) = 1/root 2 and cos^2(α) = 1/2β = π/3, therefore, cos(β) = 1/2 and cos^2(β) = 1/4Substitute in the above equation:1/2 + 1/4 + cos^2(γ) = 1cos^2(γ) = 1 - 1/2 - 1/4cos^2(γ) = 1/4cos(γ) is 1/2 or -1/2 cos(γ)= 1/2 .......> γ = π/3for cos(γ)= -1/2 .......> γ = 2π/3


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