A vector vec{P} makes angles alpha, beta, and | vedclass

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(C) For any vector,the direction cosines satisfy the relation: $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.Using the trigonometric identity $\s

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$2$

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(C) For any vector,the direction cosines satisfy the relation: $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.Using the trigonometric identity $\sin^2 	heta = 1 - \cos^2 	heta$,we can rewrite the expression as:$(1 - \sin^2 \alpha) + (1 - \sin^2 \beta) + (1 - \sin^2 \gamma) = 1$.Rearranging the terms:$3 - (\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma) = 1$.Therefore,$\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = 3 - 1 = 2$.

$A$ vector $\vec{P}$ makes angles $\alpha, \beta,$ and $\gamma$ with the $X, Y,$ and $Z$ axes respectively. Then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = $

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