A line makes angles α, β and γ with the positive directions of the coordinate axes. If a = (sin²α)î + (sin²β)ĵ + (sin²γ)k̂ and b = î + ĵ + k̂, then what is a·b equal to?

Question

Accepted Answer

2. a·b = sin²α + sin²β + sin²γ = (1-cos²α) + (1-cos²β) + (1-cos²γ) = 3 - (cos²α + cos²β + cos²γ) = 3 - 1 = 2.

A line makes angles α, β and γ with the positive directions of the coordinate axes. If a = (sin²α)î + (sin²β)ĵ + (sin²γ)k̂ and b = î + ĵ + k̂, then what is a·b equal to?

Explanation

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