Question

A vector $\overrightarrow{p}$ is making 45${}^o$ and 60${}^o$ with +ve x and y axes respectively. Then angle made by this vector with +ve z axis is

• A. 255${}^0$
• B. 75${}^0$
• C. 30${}^0$
• D. 60${}^0$

Answer 1

The correct option is D 60${}^0$

${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1$

where $\alpha$, $\beta$ and $\gamma$ are angles made by $\overrightarrow{p}$ with x, y and z axes respectively.
Here,$\alpha ={45}^{\circ },\beta ={60}^{\circ }$

$\therefore \frac{1}{2}+\frac{1}{4}+{\cos }^2\gamma =1$
$\Rightarrow {\cos }^2\gamma =\frac{1}{4}$
$\gamma ={60}^{\circ }$