(Solved): Gandalf the Grey started in the Forest of Mirkwood at a point P with coordinates (3,0) and arrived ...

Gandalf the Grey started in the Forest of Mirkwood at a point $$P$$ with coordinates $$(3,0)$$ and arrived in the Iron Hills at the point $$Q$$ with coordinates $$(4,4)$$. If he began walking in the direction of the vector $$\mathbf{v}=3\mathbf{i}+2\mathbf{j}$$ and changes direction only once, when he turns at a right angle, what are the coordinates of the point where he makes the turn?