Discussion Forum

If a line makes angle $120^{0}$ and $60^{0}$ with the positive directions of X and Z -axes respectively, then the angle made by the line  with a positive Y-axis is 

Answer:

Explanation:

Let angles $\alpha, \beta, \gamma$  makes positive direction of X,Y and Z  axes, respectively,

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

Here, $\alpha$= $120^{0}$   and $\gamma$ =$60^{0}$

 $ \therefore$   $\cos^{2}120^{0}+\cos^{2}\beta+\cos^{2}60^{0}=1$

$\Rightarrow$   $(\frac{1}{2})^{2}+\cos^{2}\beta+(\frac{1}{2})^{2}=1$

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

$\Rightarrow$     $\cos^{}\beta=\frac{\pm 1}{\sqrt{2}}$

$\Rightarrow$   $\beta$=$135^{0}$