# Vector divide with negative ratio?

1. Oct 6, 2015

### terryds

1. The problem statement, all variables and given/known data

Find the position vector of point P if P divides AB in the ratio 5:-2 given A (-1,6,4) and B (4,1,-1)

3. The attempt at a solution

The only trouble I have is to understand the question...

Does it mean something like

A------------------>B<----------------------P
3 2

Or

A----------------->P<-----------------------B
5 2

2. Oct 6, 2015

### andrewkirk

What strange terminology! I've not seen anybody use ratios with vectors that way before.
I can only guess that when they say 'P divides AB in the ratio r:s' they mean
$$\frac{\vec{AP}}{r}=\frac{\vec{PB}}{s}$$

Which of your two options does that favour?

3. Oct 7, 2015

### terryds

Hmm... I just don't understand what the negative sign means...
Is it really strange to use ratio with vectors? It's on the subchapter "Ratio Theorem" in Vector chapter.