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

The linear velocity of a rotating body is given by $\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$ 

As $\overrightarrow{\omega }=\hat{i}-2\hat{j}+2\hat{k}$  and $\overrightarrow{r}=4\hat{j}-3\hat{k}$

$\overrightarrow{v}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& -2& 2\\ 0& 4& -3\end{array}\right|$

Opening by the Ist column,

$=\hat{i}[(-2)(-3)-\left(4\right)\left(2\right)]-1(-3)\widehat{j)}+4\hat{k})$

$\overrightarrow{v}=-2\hat{i}+3\hat{j}+4\hat{k}$

$\left|\overrightarrow{v}\right|=\sqrt{2^2+3^2+4^2}=\sqrt{29}$ .