If a line makes angles 90^{circ}, 60^{circ} a | vedclass

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Question

(A) The direction cosines of a line are given by $l = \cos \alpha$,$m = \cos \beta$,and $n = \cos \gamma$,where $\alpha, \beta, \gamma$ are the angles

Vedclass · Accepted Answer

$0, \frac{1}{2}, \frac{\sqrt{3}}{2}$

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(A) The direction cosines of a line are given by $l = \cos \alpha$,$m = \cos \beta$,and $n = \cos \gamma$,where $\alpha, \beta, \gamma$ are the angles made by the line with the positive directions of the $x, y,$ and $z$-axes respectively.Given $\alpha = 90^{\circ}, \beta = 60^{\circ}, \gamma = 30^{\circ}$.Therefore,$l = \cos 90^{\circ} = 0$.$m = \cos 60^{\circ} = \frac{1}{2}$.$n = \cos 30^{\circ} = \frac{\sqrt{3}}{2}$.Thus,the direction cosines are $0, \frac{1}{2}, \frac{\sqrt{3}}{2}$.

If a line makes angles $90^{\circ}, 60^{\circ}$ and $30^{\circ}$ with the positive direction of $x, y$ and $z$-axes respectively,find its direction cosines.

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