If a vector makes angles α, β, γ with the positive direction of x, y, z axes respectively, then sin²α + sin²β + sin²γ is equal to:

If a vector makes angles α, β, γ with the positive direction of x, y, z axes respectively, then sin²α + sin²β + sin²γ is equal to:

• A. 0
• B. 1
• C. 2
• D. 3

Answer: C) 2

Explanation: We know cos²α + cos²β + cos²γ = 1. Replacing cos²θ with 1 − sin²θ gives (1−sin²α) + (1−sin²β) + (1−sin²γ) = 1. Thus, 3 − (sin²α + sin²β + sin²γ) = 1, leading to sin²α + sin²β + sin²γ = 2.