Math Help - Easy Vector Question

1. Easy Vector Question

Alright this seems a pretty easy vector question, just wondering if it's me or the solutions I've got that are wrong.

If P and Q are the points with position vectors p = −i+3j+2k and q = i−7j+4k respectively, find the position vector of the mid-point of the line PQ.
First I found the line PQ, this is equal to q-p which can easily be calculated to be 2x-10y+2z. The midpoint is just half of this which is x-5y+z.

In the solutions however they have used p+q to calculate the line PQ, is there something obvious I'm missing?

Thanks in advance to the person who sorts this annoying little problem out for me

2. q-p is a relative vector for the path from p to q. It is not a position vector for anything on that line, unless you pick one that is.

Look at it in one dimension.

p = 5
q = 2

(5-2)/2 = 3/2 = 1.5 -- That can't be half way between 2 and 5

(5+2)/2 = 7/2 = 3.5 -- That is half way between 2 and 5.

Don't you have a definition of a "position vector"? Something about beginning at the Origin should come to mind.

3. Ahh I see, thank you.