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  4. A line making angles 45° and 60° with the positive directions of the axes of x and y makes with the positive direction of z-axis, an angle of

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Q. A line making angles $45^°$ and $60^°$ with the positive directions of the axes of $x$ and $y$ makes with the positive direction of $z$-axis, an angle of

VITEEEVITEEE 2011

Solution:

Let $\gamma$ is the required angle, then
$\cos ^{2} 45^{\circ}+\cos ^{2} 60^{\circ}+\cos ^{2} \gamma=1$
$\Rightarrow \frac{1}{2}+\frac{1}{4}+\cos ^{2} \gamma=1$
$\Rightarrow \cos ^{2} \gamma=\frac{1}{2}$
$\Rightarrow \gamma=60^{\circ}$