The direction cosines of a line which makes e | vedclass

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(C) Let the direction cosines of the line be $(l, m, n) = (\cos \alpha, \cos \beta, \cos \gamma)$.
We know that for any line,the sum of the squares o

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Let the direction cosines of the line be $(l, m, n) = (\cos \alpha, \cos \beta, \cos \gamma)$.
We know that for any line,the sum of the squares of its direction cosines is $l^2 + m^2 + n^2 = 1$.
Given that the line makes equal angles with the coordinate axes,we have $\alpha = \beta = \gamma$.
Therefore,$\cos \alpha = \cos \beta = \cos \gamma$.
Substituting this into the identity,we get $\cos^2 \alpha + \cos^2 \alpha + \cos^2 \alpha = 1$.
$3 \cos^2 \alpha = 1 \Rightarrow \cos^2 \alpha = \frac{1}{3}$.
Thus,$\cos \alpha = \pm \frac{1}{\sqrt{3}}$.
Hence,the direction cosines are $(\pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}})$.

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

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