An object moves along a straight line path from P to Q under the action of a force (4 3 3 ) N. I j k − + If the coordinates of P and Q, in metres, are (3, 3, -1) and (2, -1, 4) respectively, then the work done by the force is

1 Nm

Explanation:

Given;

Force = F = (4, 3, 3)N

Position 1 = P = (3, 3, -1)m

Position 2 = Q = (2, -1, 4)m

The object moves along a straight line path from P to Q, therefore, the distance vector (d) is given by;

d = Q - P

d = (3, 3, -1) - (2, -1, 4)

d = (1, 4, -5)m

Now the work done (W) by the force (F) to move through the distance (d) is the dot product of the two vectors: F and d. i.e

W = F . d

For clarity, let's write vectors F and d in vector unit notation as follows;

F = 4 i + 3 j + 3 k

d = 1 i + 4 j - 5k

Therefore,

W = (4 i + 3 j + 3 k ) . (1 i + 4 j - 5k)

W = (4 + 12 - 15)

W = 1

Therefore, the workdone by the force is 1 Nm