Find the direction cosines of a line which ma | vedclass

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

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

Vedclass · Answer

(A) Let the direction cosines of the line be $l, m, n$. Since the line makes equal angles $\alpha$ with the coordinate axes,we have $l = \cos \alpha$,$m = \cos \alpha$,and $n = \cos \alpha$.We know that $l^2 + m^2 + n^2 = 1$.Substituting the values,we get $\cos^2 \alpha + \cos^2 \alpha + \cos^2 \alpha = 1$.This simplifies to $3 \cos^2 \alpha = 1$,which implies $\cos^2 \alpha = \frac{1}{3}$.Therefore,$\cos \alpha = \pm \frac{1}{\sqrt{3}}$.Thus,the direction cosines are $\pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}$.

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

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