If a line in octant OXYZ makes equal angles w | vedclass

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(C) Let the direction cosines of the line be $l, m, n$. Since the line makes equal angles $\alpha$ with each of the coordinate axes,we have $l = \cos

Vedclass · Accepted Answer

$l=m=n=\frac{1}{\sqrt{3}}$

Vedclass · Answer

(C) Let the direction cosines of the line be $l, m, n$. Since the line makes equal angles $\alpha$ with each of the coordinate axes,we have $l = \cos \alpha$,$m = \cos \alpha$,and $n = \cos \alpha$. We know that for any line,$l^2 + m^2 + n^2 = 1$. Substituting the values,we get $\cos^2 \alpha + \cos^2 \alpha + \cos^2 \alpha = 1$. $3 \cos^2 \alpha = 1 \Rightarrow \cos^2 \alpha = \frac{1}{3}$. Since the line is in the first octant $OXYZ$,the direction cosines must be positive,so $\cos \alpha = \frac{1}{\sqrt{3}}$. Thus,$l = m = n = \frac{1}{\sqrt{3}}$.

If a line in octant $OXYZ$ makes equal angles with coordinate axes,then

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