Work is force times distance. A force is applied on an object over a distance. It must be displaced for work to be done. Therefore, standing in the same spot holding a box, without moving means no work is done on that body. However, if you carry that box from point A to point B, work is done in Joules.

First of all.

Work is defined as the scalar product of force and displacement.

W = F.s

Therefore it is a scalar, it is not a vector. So you just add them up and you dont take a sign into account.

Therefore total work you done = Work from home to office+ work from office to home.

They add up, they dont cancel out.

Energy is also the same. It is a scalar too, not a vector.

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