In unit vector notation, find the torque about a point at coordinates (2.0 m, 1.0 m, 3.0 m) on a particle located at (3.0 m, 1.0 m, 2.0 m) when a force `vecF=(1.0N)hati-(3.0N)hatk` acts on the particle.

Explanation

To find the torque about a point at coordinates (2.0 m, 1.0 m, 3.0 m) on a particle located at (3.0 m, 1.0 m, 2.0 m) when a force \(\vec{F} = (1.0 \, \text{N}) \hat{i} - (3.0 \, \text{N}) \hat{k}\) acts on the particle, we can follow these steps:

### Step 1: Calculate the position vector \(\vec{r}\)
The position vector \(\vec{r}\) from the point (2.0 m, 1.0 m, 3.0 m) to the particle at (3.0 m, 1.0 m, 2.0 m) is given by:
\[ \vec{r} = \vec{r}_{\text{final}} - \vec{r}_{\text{initial}} = (3.0 \hat{i} + 1.0 \hat{j} + 2.0 \hat{k}) - (2.0 \hat{i} + 1.0 \hat{j} + 3.0 \hat{k}) \]
Calculating this gives:
...