CUET · MATHS · PYQ PAPER 2025
If a line makes angles \(\alpha, \beta\) and \(\gamma\) with the positive directions of x-axis, y-axis and z-axis respectively, then \(\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma\) is equal to
- A -2
- B 1
- C 2
- D 3
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
\(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1\) \((1 - \sin^2 \alpha) + (1 - \sin^2 \beta) + (1 - \sin^2 \gamma) = 1\) \(3 - (\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma) = 1\) \(\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = 3 - 1 = 2\)
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