Motion in a Plane - Result Question 13
15. What is the linear velocity if angular velocity vector $\vec{\omega}=3 \hat{i}-4 \hat{j}+\hat{k}$ and position vector $\vec{r}=5 \hat{i}-6 \hat{j}+6 \hat{k}$
[1999]
(a) $6 \hat{i}+2 \hat{j}-3 \hat{k}$
(b) $-18 \hat{i}-13 \hat{j}+2 \hat{k}$
(c) $18 \hat{i}+13 \hat{j}-2 \hat{k}$
(d) $6 \hat{i}-2 \hat{j}+8 \hat{k}$
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Answer:
Correct Answer: 15. (b)
Solution:
- (b) As we know that
$ \begin{aligned} \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}) \\ & =-18 \hat{i}-13 \hat{j}+2 \hat{k} \end{aligned} $
