A force \( \vec{F} = \left( 7 \hat{i} + 8 \hat{k} \right) \text{ N} \) is applied to a rotating object. If the displacement vector from the pivot to the point of action is \( \vec{r} = 3 \hat{i} \text{ m}, \) what is the torque?

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Consider two vectors \( \vec{r} = 3 \hat{j} \text{ m} \) and \( \vec{F} = \left( 6 \hat{i} + 9 \hat{k} \right) \text{ N}. \) What is the torque in unit vector form?

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A force of \( \vec{F} = \left(3 \hat{i} + 6 \hat{j} \right) \text{ N} \) is applied to a disc, as shown in the figure above. The displacement vector from the center of the disc to the force's point of action is \( \vec{r} = \left( 7 \hat{i} + 3\hat{j} \right) \text{ m}. \) Find the torque produced by the force \(\vec{F}.\)

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Forces \( \vec{F_1} = \left( 6 \hat{i} + 9 \hat{j} \right) \text{ N} \) and \( \vec{F_2} = \left( 9 \hat{i} + 14 \hat{j} \right) \text{ N} \) are applied to a disc, as shown in the figure above. The displacement vectors from the center of the disc to the points of action of forces \( \vec{F_1} \) and \(\vec{F_2}\) are \( \vec{r_1} = 9 \hat{i} \text{ m} \) and \( r_2 = 5 \hat{j} \text{ m}, \) respectively. Find the net torque produced by the forces.

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A plum is located at \( ( 9 \text{ m}, 12 \text{ m} )\) on the \(xy\)-coordinate plane. If a force of \( \vec{F} = ( 4 \text{ N} , 8 \text{ N} )\) is applied to the plum, what is the torque relative to the origin \(O?\)

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