Question

Find the angle between the vectors $\hat{i}+\hat{j}$ and $\hat{j}-\hat{k}$.

Answer 1

given vectors

$\overrightarrow{a}=\hat{i}+\hat{j}$

$\overrightarrow{b}=\hat{j}-\hat{k}$

$\overrightarrow{a}\cdot \overrightarrow{b}=\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\cos \theta$

$(\hat{i}+\hat{j})\cdot (\hat{j}-\hat{k})=\sqrt{1^2+1^2}\sqrt{1^2+1^2}\cos \theta$

$1=\sqrt{2}\sqrt{2}\cos \theta$

$1=2\cos \theta$

$\theta ={\cos }^{-1}\left(\frac{1}{2}\right)$

$\theta ={60}^{.}=\frac{\pi }{3}$