Work = Dot product of Force and Displacement

W = F.D

F_{1} = 2i + 3j , W_{1} = 8J , D_{1} = ?

W_{1} = F_{1}.D_{1}

Let the displacement vector D_{1} have components xi + yj

8 = (2i + 3j).(xi + yj)

8 = (2i.xi) + (2i.yj) + (3j.xi) + (3j.yj)

8 = 2x + 3y

F_{2} = 3i + 5j , W_{2} = -4 J , D_{2} = ?

W_{2} = F_{2}.D_{2}

Let the components of D_{2} = ai + bj

-4 = (3i + 5j).(ai + bj)

-4 = (3i.ai) + (3i.bj) + (5j.ai) + (5j.bj)

-4 = 3a + 5b