Question

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

• A. $60^{°}$
• B. $120^{°}$
• C. $60^{°}$ or $120^{°}$
• D. None of these

Answer 1

Answer: (A)

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