Find the torque of a force F = −3î + ĵ + 5k̂ acting at the point r = 7î + 3ĵ + k̂.

Question

Accepted Answer

14î − 38ĵ + 16k̂. Torque is given by the cross product $ \vec{\tau} = \vec{r} \times \vec{F} $. Using the determinant method, $ \vec{\tau} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 7 & 3 & 1 \ -3 & 1 & 5 \end{vmatrix} = \hat{i}(3 \cdot 5 - 1 \cdot 1) - \hat{j}(7 \cdot 5 - (-3) \cdot 1) + \hat{k}(7 \cdot 1 - 3 \cdot (-3)) = 14\hat{i} - 38\hat{j} + 16\hat{k} $. Thus, the correct answer is D.

Find the torque of a force F = −3î + ĵ + 5k̂ acting at the point r = 7î + 3ĵ + k̂.

Solution

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