Physics - Rotation Question with Solution | TestHub

As we know that

$\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}=(3\hat{\mathrm{i}}-4\hat{\mathrm{j}}+\hat{\mathrm{k}})\times (5\hat{\mathrm{i}}-6\hat{\mathrm{j}}+6\hat{\mathrm{k}})$

$\begin{array}{l}\therefore \overrightarrow{w}\times \overrightarrow{r}=\left|\begin{array}{ccc}\hat{\mathrm{i}}& \hat{\mathrm{j}}& \hat{\mathrm{k}}\\ 3& -4& 1\\ 5& -6& 6\end{array}\right|\\ \mathrm{or}\overrightarrow{w}\times \overrightarrow{r}=\hat{\mathrm{i}}(-24+6)+\hat{\mathrm{j}}(5-18)+\hat{\mathrm{k}}(-18+20)\end{array}$

$=-18\hat{\mathrm{i}}-13\hat{\mathrm{j}}+2\hat{\mathrm{k}}$