Say you have two forces (2i+3j)N and (pi+qj)N acting on the particle P, given that the resultant of the two forces R, is parallel to to the vector (-i+4j). How would you show that 4p +q+11=0?
I know that the resultant force is $(2+p,3+q)$ and know that a parallel vectors have a factor but I don't know what to do next.
Hint:
The resultant force is $(2+p)\mathbf{i}+(3+q)\mathbf{j}$ (by adding each term). $(2+p)\mathbf{i}+(3+q)\mathbf{j}$ is parallell to $-\mathbf{i}+4\mathbf{j}$ if you can find a number $s\in\mathbb{R}$ such that: $$s\left ( (2+p)\mathbf{i}+(3+q)\mathbf{j}\right )=-\mathbf{i}+4\mathbf{j}$$