For a body angular velocity ω→=i^−2j^+3k^ and radius vector is r→=i^+j^+k^ then its velocity is :

v→=ω→×r→=i^j^k^1−23111=i^(−2−3)−j^(1−3)+k^(1+2)=−5i^+2j^+3k^

For a body angular velocity ω→=i^−2j^+3k^ and radius vector is r→=i^+j^+k^ then its velocity is :

v→=ω→×r→=i^j^k^1−23111=i^(−2−3)−j^(1−3)+k^(1+2)=−5i^+2j^+3k^

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For a body angular velocity $\vec{ω} = \hat{i} - 2 \hat{j} + 3 \hat{k}$ and radius vector is $\vec{r} = \hat{i} + \hat{j} + \hat{k}$ then its velocity is :

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$- 5 \hat{i} + 2 \hat{j} + 3 \hat{k}$

$- 5 \hat{i} + 2 \hat{j} - 3 \hat{k}$

$- 5 \hat{i} - 2 \hat{j} + 3 \hat{k}$

$- 5 \hat{i} - 2 \hat{j} - 3 \hat{k}$

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Detailed Solution

$\begin{array}{l} \vec{v} = \vec{ω} \times \vec{r} = |\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 1 & - 2 & 3 \\ 1 & 1 & 1 \end{array}| = \hat{i} (- 2 - 3) - \hat{j} (1 - 3) + \hat{k} (1 + 2) \\ = - 5 \hat{i} + 2 \hat{j} + 3 \hat{k} \end{array}$