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

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(B) The direction cosines of a line are $l = \cos \alpha$,$m = \cos \beta$,and $n = \cos \gamma$. We know that $l^2 + m^2 + n^2 = 1$,which implies $\c

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$-1$

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(B) The direction cosines of a line are $l = \cos \alpha$,$m = \cos \beta$,and $n = \cos \gamma$. We know that $l^2 + m^2 + n^2 = 1$,which implies $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$. Using the identity $\cos 2	heta = 2 \cos^2 	heta - 1$,we can write: $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = (2 \cos^2 \alpha - 1) + (2 \cos^2 \beta - 1) + (2 \cos^2 \gamma - 1)$ $= 2(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma) - 3$ $= 2(1) - 3$ $= 2 - 3 = -1$.

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

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