If a line makes angles 90^{circ}, 135^{circ} | vedclass

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(B) The direction cosines of a line making angles $\alpha, \beta, \gamma$ with the positive $X, Y$ and $Z$ axes are given by $\cos \alpha, \cos \beta,

Vedclass · Accepted Answer

$\left(0, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$

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(B) The direction cosines of a line making angles $\alpha, \beta, \gamma$ with the positive $X, Y$ and $Z$ axes are given by $\cos \alpha, \cos \beta, \cos \gamma$.Here,$\alpha = 90^{\circ}, \beta = 135^{\circ}, \gamma = 45^{\circ}$.The direction cosines are:$l = \cos 90^{\circ} = 0$$m = \cos 135^{\circ} = \cos(180^{\circ} - 45^{\circ}) = -\cos 45^{\circ} = -\frac{1}{\sqrt{2}}$$n = \cos 45^{\circ} = \frac{1}{\sqrt{2}}$Thus,the direction cosines are $\left(0, -\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$.

If a line makes angles $90^{\circ}, 135^{\circ}$ and $45^{\circ}$ with the positive $X, Y$ and $Z$ axis respectively,then its direction cosines are

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