Question

What is the value of linear velocity. If $\overrightarrow{\omega }=3\hat{i}+4\hat{j}+\hat{k}$ and $\overrightarrow{r}=5\hat{i}-6\hat{j}+6\hat{k}$

Answer 1

$\overrightarrow{v}=\overrightarrow{w}\times \overrightarrow{r}=(3\hat{i}+4\hat{j}+\hat{k})\times (5\hat{i}-6\hat{j}+6\hat{k})=\begin{array}{ccc}i& j& k\\ 3& 4& 1\\ 5& -6& 6\end{array}=i\left|\begin{array}{cc}4& 1\\ -6& 6\end{array}\right|-j\left|\begin{array}{cc}3& 1\\ 5& 6\end{array}\right|+k\left|\begin{array}{cc}3& 4\\ 5& -6\end{array}\right|=i(24+6)-j(18-5)+k(-18-20)=30\hat{i}-13\hat{j}-38\hat{k}v=\sqrt{{\left(30\right)}^2+{\left(13\right)}^2+{\left(38\right)}^2}v=50m/s$