If force vec{F} = 3 hat{i} + 4 hat{j} - 2 hat | vedclass

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(B) The torque $\vec{	au}$ is given by the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$:$\vec{	au} = \vec{r} 	imes

Vedclass · Accepted Answer

$-10 \hat{i} + 10 \hat{j} + 5 \hat{k}$

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(B) The torque $\vec{	au}$ is given by the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$:$\vec{	au} = \vec{r} 	imes \vec{F}$Using the determinant form for the cross product:$\vec{	au} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 2 & 1 & 2 \ 3 & 4 & -2 \end{vmatrix}$Expanding the determinant:$\vec{	au} = \hat{i} [(1)(-2) - (2)(4)] - \hat{j} [(2)(-2) - (2)(3)] + \hat{k} [(2)(4) - (1)(3)]$$\vec{	au} = \hat{i} [-2 - 8] - \hat{j} [-4 - 6] + \hat{k} [8 - 3]$$\vec{	au} = -10 \hat{i} + 10 \hat{j} + 5 \hat{k}$

If force $\vec{F} = 3 \hat{i} + 4 \hat{j} - 2 \hat{k}$ acts on a particle having position vector $\vec{r} = 2 \hat{i} + \hat{j} + 2 \hat{k}$,then the torque about the origin will be:

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