The angular velocity of a rotating body is $\vec{ω} = 4 \hat{i} + \hat{j} - 2 \hat{k}$ . The linear velocity of the body whose position vector $2 \hat{i} + 3 \hat{j} - 3 \hat{k}$ is

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$5 \hat{i} + 8 \hat{j} + 14 \hat{k}$

$3 \hat{i} + 8 \hat{j} + 10 \hat{k}$

$8 \hat{i} - 3 \hat{j} + 2 \hat{k}$

$- 8 \hat{i} + 3 \hat{j} + 2 \hat{k}$

answer is B.

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Detailed Solution

$\bar{v} = \bar{ω} \times \bar{r} = (4 \hat{i} + \hat{j} - 2 \hat{k}) \times (2 \hat{i} + 3 \hat{j} - 3 \hat{k}) = 3 \hat{i} + 8 \hat{j} + 10 \hat{k}$

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