Final answer:
The torque about the origin on a particle located at r = 3mi+4mj-2mk with a force F = 5Ni-2Nj+3Nk can be calculated using the formula Torque = r x F. By substituting the values into the formula and calculating the cross product, we find that the torque is 22mi + 9mj - 2mk.
Step-by-step explanation:
To find the torque about the origin, we can use the formula:
Torque = r x F
Given that r = 3mi+4mj-2mk and F = 5Ni-2Nj+3Nk, we can substitute the values into the formula:
Torque = (3mi+4mj-2mk) x (5Ni-2Nj+3Nk)
To calculate the cross product, we can use the determinant method:
Torque = (4 * 3 - (-2) * 5)mi + ((-2) * 3 - (3) * 5)mj + ((3) * (-2) - (4) * (-2))mk
Torque = 22mi + 9mj - 2mk