In unit vector notation, find the net torque about the origin on a particle located at `(2.0m,-2.0m,-6.0m)` when the three forces `vecF_(1)=(6.0N)hatj,vecF_(2)=(1.0N)hati-(2.0N)hatj,andvecF_(3)=(4.0N)hati+(2.0N)hatj-(3.0N)k` act on the particle.

Explanation

To solve the problem, we need to find the net torque about the origin on a particle located at the position vector \( \vec{r} = (2.0 \, \text{m}, -2.0 \, \text{m}, -6.0 \, \text{m}) \) when three forces \( \vec{F}_1, \vec{F}_2, \) and \( \vec{F}_3 \) are acting on it. The torque \( \vec{\tau} \) is given by the cross product of the position vector \( \vec{r} \) and the net force vector \( \vec{F}_{\text{net}} \).

### Step 1: Define the position vector
The position vector \( \vec{r} \) can be expressed in unit vector notation as:
\[ \vec{r} = 2.0 \hat{i} - 2.0 \hat{j} - 6.0 \hat{k} \]

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