Question

If a line makes angles of $30°$ and $45°$ with x-axis and y-axis, then the angle made by it with z-axis is

• A. $45°$
• B. $60°$
• C. $120°$
• D. None of these

Answer 1

The correct option is B

$60°$

Explanation for the correct option:

Find the angle that line makes with z-axis:

Let the angle with z axis be $\gamma$

As we know that,

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

$\Rightarrow$${\cos }^{2}60°+{\cos }^{2}45°+\cos 2\gamma =1$

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

$\Rightarrow$ ${\cos }^2\gamma =1-\frac{1}{4}-\frac{1}{2}$

$\Rightarrow$ ${\cos }^2\gamma =\frac{1}{4}$

$\because$The angle is acute,

$\mathbf{\therefore }\mathit{\gamma }\mathbf{}\mathbf{=}\mathbf{}\mathbf{60}\mathbf{°}$

Hence, Option ‘B’ is Correct.