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Question

If a line makes angles $$90^{\circ}, 135^{\circ}, 45^{\circ}$$ with the $$x, y$$ and $$Z-\text{axes}$$ respectively, find its direction cosines.


Solution

Let the direction cosines of the line be $$l, m, n$$.
$$l=\cos {{90}^{o}}=0$$
$$m=\cos {{135}^{o}}=-\cfrac { 1 }{ \sqrt { 2 }  } $$
$$n=\cos {{45}^{o}}=\cfrac { 1 }{ \sqrt { 2 }  } $$
Therefore, the direction cosines of the line are $$0, -\cfrac{1}{\sqrt {2}}$$ and $$\cfrac{1}{\sqrt {2}}$$.

Mathematics
RS Agarwal
Standard XII

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