If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.

Question:

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

Solution:

Let direction cosines of the line be $I, m$, and $n$.

$l=\cos 90^{\circ}=0$

$m=\cos 135^{\circ}=-\frac{1}{\sqrt{2}}$

$n=\cos 45^{\circ}=\frac{1}{\sqrt{2}}$

Therefore, the direction cosines of the line are $0,-\frac{1}{\sqrt{2}}$, and $\frac{1}{\sqrt{2}}$.

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