Question

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

• A. ${150}^o$
• B. ${60}^o$
• C. ${135}^o$
• D. ${120}^o$

Answer 1

The correct option is C ${135}^o$

We know that ${cos}^2\alpha +{cos}^2\beta +{cos}^2\gamma =1$,

i.e., sum of the squares of the direcction cosines is unity,

Where $\alpha ,\beta ,\gamma$ are the angles made by a line with positive direction of the axes,

$⟹\frac{1}{4}+{cos}^2\beta +\frac{1}{4}=1⟹{cos}^2\beta =\frac{1}{2}$

$cos\beta =\frac{1}{\sqrt{2}}or-\frac{1}{\sqrt{2}}⟹\beta ={45}^{0}or{135}^0$