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If a line makes angles \(90^{\circ}, 135^{\circ}\) and \(45^{\circ}\) with the positive directions of \(X, Y, Z\)-axes respectively. Then, its direction cosines are
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The correct answer is:
\(\left(0, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
Given angles made by line with axes are
\(\alpha=90^{\circ}, \quad \beta=135^{\circ}, \quad \gamma=45^{\circ}\)
So, direction cosines are,
\(\begin{aligned}
& \cos \alpha=\cos 90^{\circ}=0 \\
& \cos \beta=\cos 135^{\circ}=-\frac{1}{\sqrt{2}} \\
& \cos \gamma=\cos 45^{\circ}=\frac{1}{\sqrt{2}}
\end{aligned}\)
\(\alpha=90^{\circ}, \quad \beta=135^{\circ}, \quad \gamma=45^{\circ}\)
So, direction cosines are,
\(\begin{aligned}
& \cos \alpha=\cos 90^{\circ}=0 \\
& \cos \beta=\cos 135^{\circ}=-\frac{1}{\sqrt{2}} \\
& \cos \gamma=\cos 45^{\circ}=\frac{1}{\sqrt{2}}
\end{aligned}\)
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