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प्रश्न
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.
पर्याय
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.
उत्तर
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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