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

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(A) Let the direction angles of the line be $\alpha = 90^{\circ}, \beta = 135^{\circ},$ and $\gamma = 45^{\circ}$.The direction cosines $(l, m, n)$ of

Vedclass · Accepted Answer

$0, -\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}$

Vedclass · Answer

(A) Let the direction angles of the line be $\alpha = 90^{\circ}, \beta = 135^{\circ},$ and $\gamma = 45^{\circ}$.The direction cosines $(l, m, n)$ of a line are given by $l = \cos \alpha, m = \cos \beta,$ and $n = \cos \gamma$.Calculating each value:$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}}$Therefore,the direction cosines of the line are $0, -\frac{1}{\sqrt{2}},$ and $\frac{1}{\sqrt{2}}$.

If a line makes angles $90^{\circ}, 135^{\circ},$ and $45^{\circ}$ with the $x, y,$ and $z$-axes respectively,find its direction cosines.

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