What is the net torque on this object?

The link for the image doesn't work for me. However, my guess is that some of the torques are negative because they oppose the other torque. If your question is why the first is positive and the last two negative instead of the first negative and the last two positive then the answer is because there is a sign convention, called the right hand rule, with the cross product. E.g. the reason that i x j = k instead of -k is purely a convention (where i is a unit vector in the x direction, j a unit vector in the y direction, and k a unit vector in the z direction).

 

Are you familiar with the right hand rule? If into your computer screen is the negative direction and out is the positive direction then all of the signs are correct.

 

Hi BrooklynBees,

If you were not taught the right hand rule, then the usual convention is that clockwise torques are considered to be negative and counter-clockwise torques are positive. The equation in your post then indicates that the torque from the 10 N force is counterclockwise, and the torques from the other two forces are clockwise. Can you see how that matches the diagram?