A body is acted upon by 3 forces, F1 of magnitude 5 unit in d direction of (6,2,3), ... see the details below?

Question

A body is acted upon by three forces, F1 of magnitude 5 units in the direction of (6,2,3), F2 of magnitude 3 units in the direction of (3, -2 ,6) and F3 of magnitude 1 unit in the direction of (2, -3, -6).
(i) Obtain the resultant force, F
(ii) Find the magnitude of F
(iii) Find the work done in displacing the body from A(2, -1, -3) to B(5,-1,-1) under the influence of F.

Answer 1

First divide each direction vector by its own magnitude*. These are called unit vectors (magnitudes = 1). Then multiply each unit vector by the magnitudes given in the problem. These are the actual force vectors. Then add the three up. That's the resultant force vector F (q. i). Find its maagnitude (q. ii).

Subtract A from B. That's the net displacement C. Take the dot product** of F and C, preserving sign. That's the work done on the body. Note that a dot product can be + or -. (q. iii).

*Magnitude of vector (x,y,z) = sqrt(x^2 + y^2 + z^2)
**Dot product of vectors (u,v,w) and (x,y,z) = u*x + v*y + w*z