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

This question has appeared in model paper 2012

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• Sum of the squares of the direction cosines is one.
We know sum of the squares of the direction cosines is one.
$(ie)\cos ^2 \alpha +\cos ^2 \beta+\cos ^2 \gamma=1$
But it is given that $\alpha=\beta=\gamma$
Therefore $\cos ^2 \alpha +\cos ^2 \alpha+\cos ^2 \alpha=1$
$=>3 \cos ^2 \alpha=1$
Therefore $\cos ^2 \alpha=\large\frac{1}{3}$
$=>\cos \alpha=\pm \large\frac{1}{\sqrt 3}$
Hence the direction cosines are $\bigg(\pm\large \frac{1}{\sqrt 3},\pm \large\frac{1}{\sqrt 3},\pm \large\frac{1}{\sqrt 3} \bigg)$
answered Jun 3, 2013 by