Final answer:
The torque about the origin on a particle can be calculated using the cross product of the position vector and the force vector. In this case, the torque is equal to (-8k - 6i - 23j) N·m.
Step-by-step explanation:
The torque about the origin on a particle located at → r = (3ᵧ + 4ʒ - 2ᵯ) m exerted by a force → f = (5ᵧ - 2ʒ + 3ᵯ) n can be calculated using the cross product of the position vector r and the force vector f. The torque is given by the formula: τ = r x f. In this case, the torque is equal to (3ᵧ + 4ʒ - 2ᵯ) x (5ᵧ - 2ʒ + 3ᵯ). To calculate the torque, we can use the determinant of the matrix formed by the components of the position and force vectors:
τ = | i j k |
| 3 4 -2 |
| 5 -2 3 |
= (-8ᵯ - 6ᵧ - 23ʒ) N·m.