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  4. If the directions cosines of a line are k, k, k, then

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Q. If the directions cosines of a line are $k$, $k$, $k$, then

Three Dimensional Geometry

Solution:

$(k, k, k) $is direction cosines of a line. Then,
$k^{2}+k^{2}+k^{2}=1$
$\Rightarrow 3k^{2}=1$
$\Rightarrow k^{2}=\frac{1}{3}$
$\Rightarrow k=\pm\frac{1}{\sqrt{3}}$