Thanks Spanky

I suspected that vectors were involved after trolling through umpteen pages of online parallelogram related problems. I also use a site that has actual completed exam papers. What was throwing me was the negative signs. The specimen exam answer is underneath. I won’t lie I’m going to have to study this with the lad and go back over vectors. I’m sure once we get our heads around the positive a negative signs all will become apparent

If it helps, a vector is just a series of instructions on how to get from one point to another and they are directional. This direction is denoted by an arrow on the diagram.

So for sake of argument in the diagram, vector

__a__ contains the instructions to go from point B to point A. This could be something like go ten metres North then 1 metre East (the exact numbers don't matter, but might help you understand). Now vector

__a__ is not locked to any position it's just an instruction that can be applied to any point to move 10m North and 1m East.

Now if

__a__ is the instruction to get from B to A, then what if I want to get from A to B? Clearly I need to go in the opposite direction (ten metres South and 1 metre West), which is -

__a__ effectively if you go in the opposite direction to the vector direction on the diagram (against the arrow on the diagram) then you multiply the vector by -1

So when we move from one point to another (to solve the original problem) we need to look at whether we are following the arrows or not.

So if I go from B to E, I am following the vector from B to A and A to E, so I simply add the vector together (

**a** + 2

__b__) since I am following the arrow.

But if I wish to go from E to B, I go from E to A ( -2

__b__ ) and the from A to B ( -

__a__ ), both against the arrow, giving -

__a__ - 2

__b__.

Hope this helps!