Find the torque of a force vec{F} = 7 hat{i} | vedclass

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Question

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

Vedclass · Accepted Answer

$2 \hat{i} + 12 \hat{j} + 10 \hat{k}$

Vedclass · Answer

(A) The torque $\vec{	au}$ is given by the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$ as $\vec{	au} = \vec{r} 	imes \vec{F}$.Given $\vec{r} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{F} = 7 \hat{i} + 3 \hat{j} - 5 \hat{k}$.Using the determinant method:$\vec{	au} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & -1 & 1 \ 7 & 3 & -5 \end{vmatrix}$$\vec{	au} = \hat{i}((-1)(-5) - (1)(3)) - \hat{j}((1)(-5) - (1)(7)) + \hat{k}((1)(3) - (-1)(7))$$\vec{	au} = \hat{i}(5 - 3) - \hat{j}(-5 - 7) + \hat{k}(3 + 7)$$\vec{	au} = 2 \hat{i} + 12 \hat{j} + 10 \hat{k}$.

Find the torque of a force $\vec{F} = 7 \hat{i} + 3 \hat{j} - 5 \hat{k}$ about the origin. The force acts on a particle whose position vector is $\vec{r} = \hat{i} - \hat{j} + \hat{k}$.

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