Question

If the position vector of a particle is $\hat{r}=(3\hat{i}-4\hat{j})$ meter and its angular velocity is $\overline{\omega }=(\hat{j}-2\hat{k})rad/sec$ then its linear velocity is (in m/s)

• A. $-(8\hat{i}+6\hat{j}+3\hat{k})$
• B. $(3\hat{i}-6\hat{j}+8\hat{k})$
• C. $-(3\hat{i}-6\hat{j}+6\hat{k})$
• D. $(6\hat{i}-8\hat{j}+3\hat{k})$

Answer 1

The correct option is A $-(8\hat{i}+6\hat{j}+3\hat{k})$

We have $v=\omega \times r$
or
$v=\left|\begin{array}{ccc}i& j& k\\ 0& 1& -2\\ 3& -4& 0\end{array}\right|$
or
$v=-(8i+6j+3k)$