Question

Find the cosine of the angle between the vectors:
$\overline{a}=4\hat{i}+3\hat{k},\overline{b}=\hat{i}-2\hat{j}+2\hat{k}$

Answer 1

Let the angle between them be $\theta$

Given $\overline{a}=4\hat{i}+3\hat{k},\overline{b}=\hat{i}-2\hat{j}+2\hat{k}$

As we know that $\overrightarrow{a}\cdot \overrightarrow{b}=|\overrightarrow{a}||\overrightarrow{b}|\cos \theta$

$\cos \theta =\frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{a}||\overrightarrow{b}|}=\frac{(4\hat{i}+3\hat{k}).(\hat{i}-2\hat{j}+2\hat{k})}{\sqrt{4^2+3^2}\sqrt{1^2+2^2+2^2}}=\frac{4+0+6}{15}=\frac{2}{3}$