particle of mass m kilograms is acted on by two forcesF[1]andF[2]with magnitudes3*sqr-root 5newtons andsqr-root 5newtons and directions parallel to the vectorsi+2jandi-2jrespectively.

The particle is initially at a position given by the vector2i+j

i was told to calculate the cartesian components ofF[1]andF[2]and hence calculate the total forceF[1] + F[2],acting on the particle in component form

MY SOLUTION

The vector i+ 2j has length sqrt{1^2+ 2^2}= sqrt{5}[

A vector in that direction, with length is just 3 times that: 3i+ 6j. That's the first force vector.

Similarly, the vector i- 2j also has length root5 so that is the second force vector. The total force, then, is F1+ F2= (3i+ 6j)+ (i- 2j)= 4i+4j

from there i need toshow the couple of the total force about the point with position vector i is zero.....so the total force is 4i+4j............................

I would appreaciate a explanation to how to tackle this Q, so I can do it myself................but im assuming that it is a single force and a couple cannot be put in equilibrium by a single force so it must be zero? is that correct???????