Question

Let a vector $\overrightarrow{r}$ make angles ${60}^o,{30}^o$ with it and y-axes respectively.Find the angle $\overrightarrow{r}$ make with z-axis.

• A. ${30}^o$
• B. ${60}^o$
• C. ${90}^o$
• D. ${120}^o$

Answer 1

Answer: (C)

${90}^o$

Sum of squares of direction cosines $=1$

$l^2+m^2+n^2=1$

Here, $l=\cos {60}^0,m=\cos {30}^0\left(given\right),n=?$

$n^2=1-l^2-m^2{n}^2=1-{\left(\frac{1}{2}\right)}^2-{\left(\frac{\sqrt{3}}{2}\right)}^2=0$

Hence, $n=0=\cos \theta$

$\Rightarrow \theta ={90}^0$