The direction co-sines of a line which makes equal acute angles with the co-ordinate axes are

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Aicharya · Accepted Answer

We know that $\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1$ and given $\alpha=\beta=\gamma$ $	herefore 3 \cos ^{2} \alpha=1 \Rightarrow \cos ^{2} \alpha=\frac{1}{3} \Rightarrow \cos \alpha=\cos \beta=\cos \gamma=\frac{1}{\sqrt{3}}$ Note: Angles are acute. So positive sign of $\frac{1}{\sqrt{3}}$ is considered.

The direction co-sines of a line which makes equal acute angles with the co-ordinate axes are

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