Question

For a body, angular velocity $\left(\overrightarrow{\omega }\right)=\hat{i}-2\hat{j}+3\hat{k}$ and radius vector $\left(\overrightarrow{r}\right)=\hat{i}+\hat{j}+\hat{k}$, then its velocity is

• A. $-5\hat{i}+2\hat{j}+3\hat{k}$
• B. $-5\hat{i}+2\hat{j}-3\hat{k}$
• C. $-5\hat{i}-2\hat{j}+3\hat{k}$
• D. $-5\hat{i}-2\hat{j}-3\hat{k}$

Answer 1

The correct option is A $-5\hat{i}+2\hat{j}+3\hat{k}$

Relation between linear velocity and angular velocity is, $\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$
$\overrightarrow{v}=(\hat{i}-2\hat{j}+3\hat{k})\times (\hat{i}+\hat{j}+\hat{k})=(-2-3)\hat{i}-(1-3)\hat{j}+(1+2)\hat{k}=-5\hat{i}+2\hat{j}+3\hat{k}$