Understanding Torque
* Torque is a rotational force that causes an object to rotate about an axis. It's a vector quantity.
* Formula: Torque (τ) = r × F, where:
* r is the position vector from the axis of rotation to the point where the force is applied.
* F is the force vector.
* "×" denotes the cross product.
Step-by-Step Calculation
1. Identify the Force Vector (F):
* F = 7i + 3j - 5k
2. Identify the Position Vector (r):
* r = i - j + k (Be careful with the signs!)
3. Calculate the Cross Product:
* We'll use the determinant method to calculate the cross product:
```
τ = | i j k |
| 1 -1 1 |
| 7 3 -5 |
```
* Expand the determinant:
* i [(−1)(-5) - (3)(1)] - j [(1)(-5) - (7)(1)] + k [(1)(3) - (7)(-1)]
* Simplify:
* τ = 2i + 12j + 10k
Result
The torque of the force about the origin is 2i + 12j + 10k (expressed in unit-vector notation).
