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Question
Assertion (A): If a line makes angles α, β, γ with positive direction of the coordinate axes, then sin2 α + sin2 β + sin2 γ = 2.
Reason (R): The sum of squares of the direction cosines of a line is 1.
Options
Both (A) and (R) are true and (R) is the correct explanation of (A).
Both (A) and (R) are true, but (R) is not the correct explanation of (A).
(A) is true, but (R) is false.
(A) is false, but (R) is true.
Solution
Both (A) and (R) are true and (R) is the correct explanation of (A).
Explanation:
∵ cos2 α + cos2 β + cos2 γ = 1
`\implies` (1 – sin2 α) + (1 – sin2 β) + (1 – sin2 γ) = 1
`\implies` 3 – (sin2 α + sin2 β + sin2 γ) = 1
`\implies` sin2 α + sin2 β + sin2 γ = 2
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