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A line makes angles of $45^{\circ}$ and $60^{\circ}$ with the positive axes of $X$ and $Y$ respectively. The angle made by the same line with the positive axis of $Z$, is
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The correct answer is:
$60^{\circ}$ or $120^{\circ}$
Given $\alpha=45^{\circ}, \beta=60^{\circ}, \gamma=?$
$\begin{array}{l}
\because \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \\
\therefore \cos ^{2} \gamma=1-\frac{1}{2}-\frac{1}{4}=\frac{1}{4} \\
\Rightarrow \mathrm{y}=60^{\circ} \text { or } 120^{\circ}
\end{array}$
$\begin{array}{l}
\because \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \\
\therefore \cos ^{2} \gamma=1-\frac{1}{2}-\frac{1}{4}=\frac{1}{4} \\
\Rightarrow \mathrm{y}=60^{\circ} \text { or } 120^{\circ}
\end{array}$
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