Question

Find a unit vector in the direction of the vector $3\overrightarrow{a}-2\overrightarrow{b}$. Where $\overrightarrow{a}=2\hat{i}+3\hat{j}+\hat{k}$ and $\overrightarrow{b}=3\hat{i}+2\hat{j}-\hat{k}$.

Answer 1

Given $\overrightarrow{a}=2\hat{i}+3\hat{j}+\hat{k}$ and $\overrightarrow{b}=3\hat{i}+2\hat{j}-\hat{k}$.

Now,

$3\overrightarrow{a}-2\overrightarrow{b}$ $=3(2\hat{i}+3\hat{j}+\hat{k})-2(3\hat{i}+2\hat{j}-\hat{k})=5\hat{j}+5\hat{k}$.

Now a unit vector in the direction of $3\overrightarrow{a}-2\overrightarrow{b}$ is

$=\frac{5\hat{j}+5\hat{k}}{5\sqrt{2}}$

$=\frac{\hat{j}+\hat{k}}{\sqrt{2}}$.