Question

Find the angle between the vectors $\overrightarrow{r_1}=(4\hat{i}-3\hat{j}+5\hat{k})$ and $\overrightarrow{r_2}=(3\hat{i}+4\hat{j}+5\hat{k})$.

Answer 1

given vector are $\overrightarrow{r_1}=(4\hat{i}-3\hat{j}+5\hat{k})$

$\overrightarrow{r_2}=(3\hat{i}+4\hat{j}+5\hat{k})$

let $\theta$ be the angle between $r_1,2_2$

then cos $\theta =\frac{\overrightarrow{r_1}.\overrightarrow{r_2}}{|\overrightarrow{r_1}||\overrightarrow{r_2}|}$

$=\frac{12-12+25}{5\sqrt{2}.5\sqrt{2}}=\frac{1}{2}$

$\Rightarrow \theta ={\cos }^{-1}\left(\frac{1}{2}\right)=\frac{\pi }{3}$ radians.