Question

What is the linear velocity if the angular velocity vector is $\vec{\omega }=3\hat{ı}-4$ $\hat{ȷ}+\hat{k}$ and position vector is $\vec{r}=5\hat{ı}$ $-6\hat{ȷ}+6\hat{k}?$

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

Answer 1

Answer: (B)

As we know that
$\vec{v}=\vec{\omega }\times \vec{r}=(3\hat{i}-4\hat{j}+\hat{k})\times (5\hat{i}-6\hat{j}+6\hat{k})$
$\therefore \vec{w}\times \vec{r}=\left|\begin{array}{ccc}\hat{ı}& \hat{ȷ}& \hat{k}\\ 3& -4& 1\\ 5& -6& 6\end{array}\right|$
or $\vec{w}\times \vec{r}=\hat{i}(-24+6)+\hat{j}(5-18)+\hat{k}(-18+20)$
$=-18\hat{i}-13\hat{j}+2\hat{k}$