The direction cosines of a line which lies in | vedclass

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(B) Direction cosines are the cosines of the angles which a line makes with the positive coordinate axes. They are represented by $\langle l, m, n \ra

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

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(B) Direction cosines are the cosines of the angles which a line makes with the positive coordinate axes. They are represented by $\langle l, m, n \rangle$ where $l, m, n$ correspond to the $x$-axis,$y$-axis,and $z$-axis respectively. The sum of the squares of the direction cosines is unity,i.e.,$l^{2} + m^{2} + n^{2} = 1$.Since the line lies in the $ZOX$ plane,it is perpendicular to the $y$-axis. Therefore,the angle made with the $y$-axis is $90^{\circ}$,so $m = \cos(90^{\circ}) = 0$.The line makes an angle of $30^{\circ}$ with the $Z$-axis,so $n = \cos(30^{\circ}) = \frac{\sqrt{3}}{2}$.Using the property $l^{2} + m^{2} + n^{2} = 1$,we substitute $m = 0$ and $n = \frac{\sqrt{3}}{2}$:$l^{2} + 0^{2} + \left(\frac{\sqrt{3}}{2}\right)^{2} = 1$$l^{2} + \frac{3}{4} = 1$$l^{2} = 1 - \frac{3}{4} = \frac{1}{4}$$l = \pm \frac{1}{2}$.Thus,the direction cosines are $\langle \pm \frac{1}{2}, 0, \frac{\sqrt{3}}{2} \rangle$.

The direction cosines of a line which lies in the $ZOX$ plane and makes an angle of $30^{\circ}$ with the $Z$-axis are

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