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 $$\cfrac{1}{\sqrt {2}}$$.MathematicsRS AgarwalStandard XII

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