Find the direction cosines of a line which ma | vedclass

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(B) Let the line make an angle $\alpha$ with each of the coordinate axes.Thus,the direction cosines are $l = \cos \alpha$,$m = \cos \alpha$,and $n = \

Vedclass · Accepted Answer

$\left( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \right)$ or $\left( -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}} \right)$

Vedclass · Answer

(B) Let the line make an angle $\alpha$ with each of the coordinate axes.Thus,the direction cosines are $l = \cos \alpha$,$m = \cos \alpha$,and $n = \cos \alpha$.We know that for any line,$l^2 + m^2 + n^2 = 1$.Substituting the values,we get $\cos^2 \alpha + \cos^2 \alpha + \cos^2 \alpha = 1$.$3 \cos^2 \alpha = 1 \implies \cos^2 \alpha = \frac{1}{3}$.Therefore,$\cos \alpha = \pm \frac{1}{\sqrt{3}}$.Thus,the direction cosines are $\left( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \right)$ or $\left( -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}} \right)$.

Find the direction cosines of a line which makes equal angles with the coordinate axes.

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