The addition of vectors is very useful for solving problems when more than one vector is involved in a calculation. This would include situations where multiple forces are acting, situations where we consider multiple velocity components, and situations where an object is displaced more than once.
Vector addition allows us to reduce many vectors into one equivalent vector, thus simplifying the problem to be solved. These slides outline vector addition and apply it to Newton’s second law. Sample problems are provided to determine the resultant force (net force), resultant velocity and total displacement.