Assertion (A ) : If a line makes angles \alpha, \beta, \gamma with positive direction of the coordinate axes, then \sin ^2 \alpha+ \sin ^2 \beta+ \sin ^2 \gamma=2. Reason (R): The sum of squares of the direction cosines of a line is 1 .

Correct Answer is : Both (A) and (R) are true and (R) is the correct explanation of (A).

CBSE Class 12 Math 2023 Outside Delhi Set 1 Solved Paper

ASSERTION-REASON BASED QUESTIONS

In the following questions

19 & 20

, a statement of Assertion (A) is followed by a statement of Reason (R).

Choose the correct answer out of the following choices :

(A) Both (A) and (R) are true and (R) is the correct explanation of (A).

(B) Both (A) and

( {\R})

are true, but

( {\R})

is not the correct explanation of (A).

(C) (A) is true, but (R) is false.

(D) (A) is false, but (R) is true.

Question : 20 of 38

Marks: +1, -0

Assertion (A ) : If a line makes angles

α, β, γ

with positive direction of the coordinate axes, then

sin \;^2 α+ sin \;^2 β+ sin \;^2 γ=2

.

Reason (R): The sum of squares of the direction cosines of a line is 1 .

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:

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