Question

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

• A. $-18\hat{i}-13\hat{j}+2\hat{k}$
• B. $30\hat{i}-13\hat{j}-2\hat{k}$
• C. $-18\hat{i}+13\hat{j}+2\hat{k}$
• D. $-30\hat{i}-13\hat{j}+38\hat{k}$

Answer 1

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

As,
$\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$
$\Rightarrow \overrightarrow{\omega }\times \overrightarrow{r}=\left[\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& -4& 1\\ 5& -6& 6\end{array}\right]$
$\Rightarrow [-4\times 6-(1\times (-6)]\hat{i}-[3\times 6-5\times 1]\hat{j}+[-6\times 3-5\times -4]\hat{k}$
$\Rightarrow -18\hat{i}-13\hat{j}+2\hat{k}$