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(A) We know that the direction cosines of a line are $\cos \alpha, \cos \beta, 	ext{ and } \cos \gamma$.For any line,the sum of the squares of the di

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) We know that the direction cosines of a line are $\cos \alpha, \cos \beta, 	ext{ and } \cos \gamma$.For any line,the sum of the squares of the direction cosines is given by the identity: $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.Using the trigonometric identity $\sin^2 	heta = 1 - \cos^2 	heta$,we can write:$\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = (1 - \cos^2 \alpha) + (1 - \cos^2 \beta) + (1 - \cos^2 \gamma)$$= 3 - (\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma)$$= 3 - 1 = 2$.Therefore,the correct value is $2$.

If $\alpha, \beta, \gamma$ are the angles that a line makes with the positive direction of the coordinate axes,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = $

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