If a line makes angles alpha, beta, gamma wit | vedclass

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(B) The direction cosines of a line are given by $l = \cos \alpha$,$m = \cos \beta$,and $n = \cos \gamma$. We know that the sum of the squares of the

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$2$

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(B) The direction cosines of a line are given by $l = \cos \alpha$,$m = \cos \beta$,and $n = \cos \gamma$. We know that the sum of the squares of the direction cosines is always $1$,i.e.,$\cos ^2 \alpha + \cos ^2 \beta + \cos ^2 \gamma = 1$. Using the trigonometric identity $\sin ^2 	heta = 1 - \cos ^2 	heta$,we can rewrite the expression as: $\sin ^2 \alpha + \sin ^2 \beta + \sin ^2 \gamma = (1 - \cos ^2 \alpha) + (1 - \cos ^2 \beta) + (1 - \cos ^2 \gamma)$ $= 3 - (\cos ^2 \alpha + \cos ^2 \beta + \cos ^2 \gamma)$ $= 3 - 1 = 2$. Thus,the value is $2$.

If a line makes angles $\alpha, \beta, \gamma$ with the positive directions of $X, Y$ and $Z$-axes respectively,then the value of $\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma=$

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