Question

A particle, acted upon by forces 4i+j-3k and 3i+j-k , is displaced from point (1,2,3) to the point (5,4,1). Find the work done on particle.

Answer 1

Ok, you have a constant net force acting on your particle. Work is given by:\[W=F*d\]where F is your net force and d is the displacement vector. We take the dot product of these vectors in finding the work. The net force is just the vector sum of your two forces:\[F=7 i+2j-4k\]Your displacement vector is:\[d=4i+2j-2k\]We have:\[W=7(4)+2(2)+(-4)(-2)=40\]So the work done is 40 joules (assuming the force is in Newton's and displacement is given in meters).