The position vector `vecr` of a particle points along the positive direction of a z axis. If the torque on the particle is (a) zero, (b) in the negative direction of x, and ( c) in the negative direction of y, in what direction is the force causing the torque?

Explanation

To solve the problem, we need to analyze the relationship between the torque, the position vector, and the force causing the torque. The position vector \(\vec{r}\) points along the positive direction of the z-axis, which can be represented as \(\vec{r} = r \hat{k}\).

### Step-by-step Solution:

1. **Understanding Torque**:
The torque \(\vec{\tau}\) is given by the cross product of the position vector \(\vec{r}\) and the force vector \(\vec{F}\):
\[
\vec{\tau} = \vec{r} \times \vec{F}
...