Use your index finger to do those exercises:

1. Go from A to C: From A to B + from B to C. With vectors:

Since P is the midpoint of AC you'll get:

2. According the method from #1 you'll get

3. You "go" from P to Q like: From P to A + from A to Q. With vectors:

4. This vector has the same direction as and half of it's length.