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. $4\hat{i}-13\hat{j}+6\hat{k}$
• B. $6\hat{i}-2\hat{j}+3\hat{k}$
• C. $6\hat{i}-2\hat{j}+8\hat{k}$
• D. $-18\hat{i}-13\hat{j}+2\hat{k}$

Answer 1

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

Relation between linear velocity and angular velocity is, $\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$
or, $\overrightarrow{v}=(3\hat{i}-4\hat{j}+\hat{k})\times (5\hat{i}-6\hat{j}+6\hat{k})=(-24+6)\hat{i}-(18-5)\hat{j}+(-18+20)\hat{k}=-18\hat{i}-13\hat{j}+2\hat{k}$