A force F=(5i+3j)N acts on a body and causes a displacement r=(7i-j)m. Determine the work done?

Answer 1

work is done by the x component of force moving in x direction and by the y component moving in y direction
(5*7) + (3*-1)
= 35 - 3
= 32 Joules

note the -3 means the force is opposite to the motion (braking, work out)

Answer 2

your text probably expressed the work as F•r