Vector divide with negative ratio?

[terryds]

Homework Statement

[/B]
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)

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 2Please help

 

[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?

 

[terryds]

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?

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.