Question

Calculate the work done by a Force of 2𝑖 − 𝑗 − 3𝑘 in moving an object from (2, 1, 3) to (9, 4, 6) where displacement is in metres.

Answer 1

$$\vec r=(9-2)\vec i+(4-1)\vec j+(6-3)\vec k$$

$$=7\vec i+3\vec j+3\vec k$$

$$W=\vec F\cdot \vec r=2(7)+(-1)(3)+(-3)(3)=2 (J)$$

If the force is measured in newtons and the displacement is measured in metres, then the work is 2 J.