What is the torque of force vec F = 2hat i - | vedclass

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(C) 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 \v

Vedclass · Accepted Answer

$17\hat i - 6\hat j - 13\hat k$

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(C) 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 $\vec r = 3\hat i + 2\hat j + 3\hat k$ and $\vec F = 2\hat i - 3\hat j + 4\hat k$,we calculate the determinant:$\vec 	au = \begin{vmatrix} \hat i & \hat j & \hat k \ 3 & 2 & 3 \ 2 & -3 & 4 \end{vmatrix}$Expanding the determinant:$\vec 	au = \hat i(2 	imes 4 - 3 	imes (-3)) - \hat j(3 	imes 4 - 3 	imes 2) + \hat k(3 	imes (-3) - 2 	imes 2)$$\vec 	au = \hat i(8 + 9) - \hat j(12 - 6) + \hat k(-9 - 4)$$\vec 	au = 17\hat i - 6\hat j - 13\hat k$

What is the torque of force $\vec F = 2\hat i - 3\hat j + 4\hat k$ acting at a point $\vec r = 3\hat i + 2\hat j + 3\hat k$ about the origin?

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