Work = Dot product of Force and Displacement
W = F.D
F1 = 2i + 3j , W1 = 8J , D1 = ?
W1 = F1.D1
Let the displacement vector D1 have components xi + yj
8 = (2i + 3j).(xi + yj)
8 = (2i.xi) + (2i.yj) + (3j.xi) + (3j.yj)
8 = 2x + 3y
F2 = 3i + 5j , W2 = -4 J , D2 = ?
W2 = F2.D2
Let the components of D2 = ai + bj
-4 = (3i + 5j).(ai + bj)
-4 = (3i.ai) + (3i.bj) + (5j.ai) + (5j.bj)
-4 = 3a + 5b