If a straight line in space is equally inclin | vedclass

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(C) Let the direction angles of the line be $\alpha, \beta, \gamma$ with the $x, y, z$ axes respectively.Since the line is equally inclined to the coo

Vedclass · Accepted Answer

$1/\sqrt{3}$

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(C) Let the direction angles of the line be $\alpha, \beta, \gamma$ with the $x, y, z$ axes respectively.Since the line is equally inclined to the coordinate axes,we have $\alpha = \beta = \gamma$.The direction cosines of the line are $l = \cos \alpha, m = \cos \beta, n = \cos \gamma$.We know that $l^2 + m^2 + n^2 = 1$.Substituting the values,we get $\cos^2 \alpha + \cos^2 \alpha + \cos^2 \alpha = 1$.$3 \cos^2 \alpha = 1$.$\cos^2 \alpha = 1/3$.$\cos \alpha = \pm 1/\sqrt{3}$.Thus,the cosine of the angle of inclination is $1/\sqrt{3}$ (considering the positive value).

If a straight line in space is equally inclined to the coordinate axes,the cosine of its angle of inclination to any one of the axes is

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