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.

Answer 1

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