Answer:
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
