Answer the following questions about torque.Let $\mathbf{r}=\overrightarrow{OP}=\mathbf{i}-\mathbf{j}+2\mathbf{k}.$ A force $\mathbf{F}=⟨10,10,0⟩$ is applied at $P.$ Find the torque about $\vec{O}$ that is produced.

Step by Step Solution: Step 1. Calculate the position vector from O to P: Step 2. r = i - j + 2k Step 3. Calculate the cross product of r and F: t = r x F Step 4. Expand the cross product using the determinant notation: Step 5. $t=\left|\begin{array}{ccc}i& j& k\\ 1& -1& 2\\ 10& 10& 0\end{array}\right|$ Step 6. $t=(20i+20j+200k)$ Step 7. Calculate the magnitude of t: |t| = $\sqrt{(20^2+20^2+200^2)}$ Step 8. $|t|=20\sqrt{21}$ Final Answer: The torque about O is $20\sqrt{21}$ units.