Home › NDA › Vectors / Direction Cosines › Question NDA 2025 · PYQ · Vectors / Direction Cosines · easy
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? Answer
The correct answer is D: 2. a·b = sin²α + sin²β + sin²γ = (1-cos²α) + (1-cos²β) + (1-cos²γ) = 3 - (cos²α + cos²β + cos²γ) = 3 - 1 = 2.
A. -2 B. -1 C. 1 D. 2 ✓ Correct a·b = sin²α + sin²β + sin²γ = (1-cos²α) + (1-cos²β) + (1-cos²γ) = 3 - (cos²α + cos²β + cos²γ) = 3 - 1 = 2.
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