Given two force 2P and P , when the first one is doubled , i.e 4P and the 8 is added to the second one i.e P+8 , the direction of the resultant remains unaltered . What is the value of P ?
N.B : I have been solved this problem over and over many times , but every time doing it again , I can't do it and had to take the solution of the exercise. But now I have no solution in my hand , so I am posting in here . Thanks in advance.
I'm not clear exactly what you are asking but will assume it is this: find $P$ such that the vectors $(2P,P)$ and $(4P,P+8)$ have the same direction.
Two vectors have the same direction if their coordinates are proportional: $$\frac{4P}{2P}=\frac{P+8}{P}\ .$$ Solving the equation gives $P=8$.