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If a line makes angles $90^{\circ}, 135^{\circ}, 45^{\circ}$ with the $x, y$ and $z$ axes respectively, find its direction cosines.
Solution:
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Verified Answer
Direction angles are $90^{\circ}, 135^{\circ}, 45^{\circ}$
Direction cosines are
$$
\begin{aligned}
&\ell=\cos 90^{\circ}=0, m=\cos 135^{\circ}=-\frac{1}{\sqrt{2}}, \\
&n=\cos 45^{\circ}=\frac{1}{\sqrt{2}},
\end{aligned}
$$
Hence, D, C's $0,-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}$
Direction cosines are
$$
\begin{aligned}
&\ell=\cos 90^{\circ}=0, m=\cos 135^{\circ}=-\frac{1}{\sqrt{2}}, \\
&n=\cos 45^{\circ}=\frac{1}{\sqrt{2}},
\end{aligned}
$$
Hence, D, C's $0,-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}$
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