Question

The linear velocity of rotating body is given by $\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}.$ If $\overrightarrow{\omega }=\hat{i}-2\hat{j}+2\hat{k}$ and $\overrightarrow{r}=4\hat{j}-3\hat{k}$, then the magnitude of $\overrightarrow{v}$ is:

• A. $\sqrt{29}$
• B. $\sqrt{31}$
• C. $\sqrt{37}$
• D. $\sqrt{41}$

Answer 1

The correct option is A $\sqrt{29}$

$\overrightarrow{v}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& -2& 2\\ 0& 4& -3\end{array}\right|$
$\overrightarrow{v}=\hat{i}[6-8]+\hat{j}[0+3]+\hat{k}[4-0]$
$\overrightarrow{v}=-2\hat{i}+3\hat{j}+4\hat{k}\Rightarrow |\overrightarrow{v}|=\sqrt{(-2{)}^2+3^2+4^2}=\sqrt{29}$ units