Vectors, finding initial point from terminal point

Question

Find an initial point A of a non-zero vector v=A->B with terminal point B(3, 4) such that v has the same direction as u = (2, 3). I don't want the answer, how do I find the answer? Thanks :D

Answer 1

One solution is $$ A+tu=B$$ thus $$A=B-tu$$ where t is a parameter which can be any non zero real number.

You have your $B$ and $u$, so you can find your $A$

Note that the answer is not unique because $u$ is the direction vector and we really need the norm of AB to find $A$ uniquely.

Answer 2

Take the points as position vectors, then the vector formed with both of them as initial/end point is the _____ of the two position vectors. And you can add/subtract an equal vector on both sides of an vector equation the same way you do with a scalar equation.