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(C) Let the direction angles of the line be $\alpha_1, \alpha_2, \alpha_3$. We are given $\alpha_1 = \alpha$,$\alpha_2 = \frac{\pi}{2} - \alpha$,and $

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$\frac{\pi}{2}$

Vedclass · Answer

(C) Let the direction angles of the line be $\alpha_1, \alpha_2, \alpha_3$. We are given $\alpha_1 = \alpha$,$\alpha_2 = \frac{\pi}{2} - \alpha$,and $\alpha_3 = \beta$.The property of direction cosines states that $\cos^2 \alpha_1 + \cos^2 \alpha_2 + \cos^2 \alpha_3 = 1$.Substituting the given values:$\cos^2 \alpha + \cos^2 \left(\frac{\pi}{2} - \alpha\right) + \cos^2 \beta = 1$Since $\cos \left(\frac{\pi}{2} - \alpha\right) = \sin \alpha$,the equation becomes:$\cos^2 \alpha + \sin^2 \alpha + \cos^2 \beta = 1$Using the identity $\cos^2 \alpha + \sin^2 \alpha = 1$,we get:$1 + \cos^2 \beta = 1$$\cos^2 \beta = 0$$\cos \beta = 0$Therefore,$\beta = \frac{\pi}{2}$.

If the angles made by a straight line with the coordinate axes are $\alpha, \frac{\pi}{2}-\alpha, \beta$,then $\beta$ is equal to

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