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:

  1. (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} $