Work Done

Step 1: Calculate the displacement vector
The displacement vector

%5Cmathbf%7Bd%7D

is given by:

%5Cmathbf%7Bd%7D%20%3D%20(x_2%20-%20x_1)%20%5Chat%7Bi%7D%20%2B%20(y_2%20-%20y_1)%20%5Chat%7Bj%7D%20%2B%20(z_2%20-%20z_1)%20%5Chat%7Bk%7D

Substituting the given values:

%5Cmathbf%7Bd%7D%20%3D%20(4%20-%202)%20%5Chat%7Bi%7D%20%2B%20(3%20-%202)%20%5Chat%7Bj%7D%20%2B%20(2%20-%201)%20%5Chat%7Bk%7D

%5Cmathbf%7Bd%7D%20%3D%202%5Chat%7Bi%7D%20%2B%20%5Chat%7Bj%7D%20%2B%20%5Chat%7Bk%7D

Step 2: Compute Work Done
The work done

W

is calculated using the dot product:

W%20%3D%20%5Cmathbf%7BF%7D%20%5Ccdot%20%5Cmathbf%7Bd%7D

W%20%3D%20(4%5Chat%7Bi%7D%20%2B%202%5Chat%7Bj%7D%20%2B%20%5Chat%7Bk%7D)%20%5Ccdot%20(2%5Chat%7Bi%7D%20%2B%20%5Chat%7Bj%7D%20%2B%20%5Chat%7Bk%7D)

Expanding the dot product:

W%20%3D%20(4%20%5Ctimes%202)%20%2B%20(2%20%5Ctimes%201)%20%2B%20(1%20%5Ctimes%201)

W%20%3D%208%20%2B%202%20%2B%201%20%3D%2011%20%5Ctext%7B%20J%7D

Step 3: Conclusion
Thus, the work done by the force is:

%5Cmathbf%7B11%20%5Ctext%7B%20J%7D%7D

Chapter Questions
1 MCQs