If alpha, beta and gamma are the angles which | vedclass

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(B) We know that $\alpha, \beta, \gamma$ are the direction angles of a line,so the direction cosines are $\cos \alpha, \cos \beta, \cos \gamma$. The s

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$2$

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(B) We know that $\alpha, \beta, \gamma$ are the direction angles of a line,so the direction cosines are $\cos \alpha, \cos \beta, \cos \gamma$. The sum of the squares of the direction cosines is given by $\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma = 1$. We want to evaluate $\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma$. Using the identity $\sin ^{2} 	heta = 1 - \cos ^{2} 	heta$,we have: $\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma = (1 - \cos ^{2} \alpha) + (1 - \cos ^{2} \beta) + (1 - \cos ^{2} \gamma)$ $= 3 - (\cos ^{2} \alpha + \cos ^{2} \beta + \cos ^{2} \gamma)$ $= 3 - 1 = 2$.

If $\alpha, \beta$ and $\gamma$ are the angles which a half ray makes with the positive direction of the axes,then $\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma$ is equal to

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