The linear velocity of a rotating body is given by \(\vec{v} = \vec{\omega} \times \vec{r},\) where \(\vec{\omega}\) is the angular velocity and \vec{r} is the radius vector. The angular velocity of a body is \vec{w} = \hat{i} - 2\hat{j} + 2\hat{k} and the radius vector \vec{r} = 4\hat{j} - 3\hat{k}, then \(\left| \vec{v} \right|\) is
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\(\vec{v} = \vec{\omega} \times \vec{r} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & -2 & 2 \\ 0 & 4 & -3 \end{vmatrix}\)
= \hat{i}(6 - 8) - \hat{j}(-3) + 4\hat{k} - 2\hat{i} + 3\hat{j} + 4\hat{k}
\(\left|\vec{v}\right| = \sqrt{(-2)^2 + (3)^2 + 4^2} = \sqrt{29} \text{ unit}\)
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