Fewpal
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​​Two forces are acting on a body. F1=2i+3j and it does 8J of work . F2=3i+5j and it does -4J on body. Find displacement of the body in form xi+yj.

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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

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