Question

The vector position of an object is given by r what is the torque acting on the object about the origin when a force f = (−12.5i hat) n acts on it? express your answer using unit vector notation.

Answer 1

Let the vector position of the object in the (x-y) plane be 
$\vec{r} = x \hat{i} + y \hat{j}$

The applied force is
$\vec{f} = -12.5 \hat{i}$

By definition, the applied torque is
$\vec{T} = \vec{r} \times \vec{f} = (x\hat{i} + y\hat{j}) \times (-12.5y \hat{i}) = 12.5\hat{k}$

Answer: $12.5y \, \hat{k}$