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

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(B) We know that for a line with direction angles $\alpha, \beta, \gamma$,the direction cosines are $\cos \alpha, \cos \beta, \cos \gamma$. According

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$-1$

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(B) We know that for a line with direction angles $\alpha, \beta, \gamma$,the direction cosines are $\cos \alpha, \cos \beta, \cos \gamma$. According to the property of direction cosines,$\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$. 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: $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = (2\cos^2 \alpha - 1) + (2\cos^2 \beta - 1) + (2\cos^2 \gamma - 1)$ $= 2(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma) - 3$ $= 2(1) - 3 = 2 - 3 = -1$.

If a line makes angles $\alpha, \beta, \gamma$ with the three-dimensional coordinate axes respectively,then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = $

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