Question

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

• A. $6\hat{i}+2\hat{j}-3\hat{k}$
• B. $-18\hat{i}-13\hat{j}+2\hat{k}$
• C. $4\hat{i}-13\hat{j}+6\hat{k}$
• D. $12\hat{i}-7\hat{j}+5\hat{k}$

Answer 1

The correct option is B $-18\hat{i}-13\hat{j}+2\hat{k}$

We know that linear velocity,
$\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$
$\overrightarrow{v}=(3\hat{i}-4\hat{j}+\hat{k})\times (5\hat{i}-6\hat{j}+6\hat{k})$
$\overrightarrow{v}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& -4& 1\\ 5& -6& +6\end{array}\right|$
$\overrightarrow{v}=\hat{i}(-24+6)-\hat{j}(18-5)+\hat{k}(-18+20)$
$\overrightarrow{v}=-18\hat{i}-13\hat{j}+2\hat{k}$

Hence option B is the correct answer.