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(B) We know that for a line making angles $\alpha, \beta, \gamma$ with the coordinate axes,the direction cosines are $\cos \alpha, \cos \beta, \cos \g

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$-1$

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(B) We know that for a line making angles $\alpha, \beta, \gamma$ with the coordinate axes,the direction cosines are $\cos \alpha, \cos \beta, \cos \gamma$. The sum of the squares of the direction cosines is given by $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$. Now,we need to evaluate $\cos 2\alpha + \cos 2\beta + \cos 2\gamma$. Using the identity $\cos 2	heta = 2\cos^2 	heta - 1$,we get: $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = (2\cos^2 \alpha - 1) + (2\cos^2 \beta - 1) + (2\cos^2 \gamma - 1)$ $= 2(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma) - 3$ Substituting the value $1$ for the sum of squares: $= 2(1) - 3 = 2 - 3 = -1$.

$A$ line makes angles $\alpha, \beta, \gamma$ with the coordinate axes,then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma$ is equal to

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