Question

A force \( \mathbf{F} = \hat{i} + 2\hat{j} + 2\hat{k} \) acts on a particle at position vector \( \mathbf{r} = 2\hat{i} + 3\hat{j} + 4\hat{k} \). Find the torque \( \tau \).

• A. \( \tau = 2\hat{i} - 4\hat{j} + 3\hat{k} \)
• B. \( \tau = 4\hat{i} - \hat{j} - 2\hat{k} \)
• C. \( \tau = -2\hat{i} + 4\hat{j} - 3\hat{k} \)
• D. \( \tau = 3\hat{i} - 2\hat{j} + 4\hat{k} \)

Hint:

The torque is the cross product of the position vector and the force vector. Be careful with the signs and components when performing the calculation.

Answer 1

The Correct Option is A

The torque is given by \( \tau = \mathbf{r} \times \mathbf{F} \). Perform the cross product calculation between the position vector and the force vector to find the torque.