If the direction cosines of a line are k, k and k, then :

Question

If the direction cosines of a line are $k$ , $k$ and $k$ , then :

Smart Achievers · Accepted Answer

(4)

Ans. $k = \frac{1}{\sqrt{3}}$ or $- \frac{1}{\sqrt{3}}$

Explanation:

Since, direction cosines of a line are $k$ , $k$ and $k$ .

$∴$ $l = k, m = k$ and $n = k$

We know that,

$l^{2} + m^{2} + n^{2} = 1$

$\Rightarrow$ $k^{2} + k^{2} + k^{2} = 1$

$\Rightarrow$ $k^{2} = \frac{1}{3}$

$∴$ $k = \pm \frac{1}{\sqrt{3}}$

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