PROBLEMS ON FORCE AND WORKDONE IN VECTOR FORM

If

is the displacement vector of a particle moved from a point to another point after applying a constant force

on the particle, then the work done by the force on the particle is

If the force has an acute angle, perpendicular angle, and an obtuse angle, the work done by the force is positive, zero, and negative respectively.

Problem 1 :

A particle acted on by constant forces

is displaced from the point (1, 2, 3) to the point (5, 4, 1) . Find the total work done by the forces

Solution :

Problem 2 :

A particle acted on by constant forces

is displaced from the point (4, -3, -2) to the point (6, 1, -3). Find the total work done by the forces.

Solution :

Problem 3 :

A particle is acted upon by the forces

is displaced from the point (1, 3, -1) to the point (4, -1, λ) . If the work done by the forces is 16 units, find the value of λ

Solution :