A constant force F = (3.0 N) i + (2.0 N) j   is exerted on an object which moves from   r₁ = (1.0 m) i - (3.0 m) j   to   r₂ = (4.0 m) i - (5.0 m) j.
What is the work done by this force on the object?

Solution:

We have constant force, which is not parallel with the displacement, so we use

W = F· s

Let's get the displacement:

s = r₂ - r₁

= [ (4.0 m) i - (5.0 m) j] - [(1.0 m) i - (3.0 m) j]

= (3.0 m) i - (2.0 m) j

Now take the dot product:

W = [(3.0 N) i + (2.0 N) j]·[ (3.0 m) i - (2.0 m) j]

recall   i·i = 1, i·j = 0   etc.

W = 9 Nm + (-4)Nm

= 5 Nm

= 5 J

Note the work-energy theorem says that work (like energy) is a scalar, i.e. it has no direction.