Mathbee · CBSE Class 12 Maths

Class 12 Three Dimensional Geometry · Assertion Reason1 Marksdirection_cosines

Class 12 Maths · Three Dimensional Geometry · Assertion Reason #23

Assertion (A): For direction angles α,β,γ, sin²α+sin²β+sin²γ=2. Reason (R): Direction cosines satisfy cos²α+cos²β+cos²γ=1.

(A) Both A and R are true, and R correctly explains A.
(B) Both A and R are true, but R does not correctly explain A.
(C) A is true but R is false.
(D) A is false but R is true.

✅ Step-by-Step Solution

Final Answer: Option (A): Both A and R are true, and R correctly explains A.

Replace each sin² by 1−cos²; the sum is 3−1=2.

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