Find the torque of a force vec F = -3hat i + | vedclass

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Question

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

Vedclass · Accepted Answer

$14\hat i - 38\hat j + 16\hat k$

Vedclass · Answer

(A) The torque $\vec{	au}$ is defined as the cross product of the position vector $\vec{r}$ and the force vector $\vec{F}$:$\vec{	au} = \vec{r} 	imes \vec{F}$Given $\vec{r} = 7\hat{i} + 3\hat{j} + \hat{k}$ and $\vec{F} = -3\hat{i} + \hat{j} + 5\hat{k}$,we calculate the cross product using the determinant method:$\vec{	au} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 7 & 3 & 1 \ -3 & 1 & 5 \end{vmatrix}$Expanding the determinant along the first row:$\vec{	au} = \hat{i}(3 	imes 5 - 1 	imes 1) - \hat{j}(7 	imes 5 - 1 	imes (-3)) + \hat{k}(7 	imes 1 - 3 	imes (-3))$$\vec{	au} = \hat{i}(15 - 1) - \hat{j}(35 + 3) + \hat{k}(7 + 9)$$\vec{	au} = 14\hat{i} - 38\hat{j} + 16\hat{k}$

Find the torque of a force $\vec F = -3\hat i + \hat j + 5\hat k$ acting at the point $\vec r = 7\hat i + 3\hat j + \hat k$ with respect to the origin.

Similar Questions

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If $\vec{F} = (4\hat{i} - 10\hat{j})$ and $\vec{r} = (5\hat{i} - 3\hat{j})$,then calculate the torque $\vec{\tau} = \vec{r} \times \vec{F}$. (in $hat{k}$)

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