Negative vectors (e.g. velocity) If you said someone had a velocity of $-12\,{\rm mph}$ and they were traveling north? Wouldn't it mean that they were traveling $12\,{\rm mph}$ south?
This is a quote from here:

if something [object-x] moving to the right was taken to have positive momentum, then one should consider something [object-y] moving to the left to have negative momentum.

But isn't momentum a vector, so the direction should be specified separately to the number. What I mean is, object-y with $-1200\,{\rm kg\, m/s}$ and object-x with 1200kg m/s should both have momentum in the same direction. But this can't be because as the quote says they are moving in opposite direction.
 A: That quote is abit misleading, momentum is a vector, however a vector is neither negative nor positive, only its components can have this characteristic. The two objects you are describing does not have the same momentum, but they have the same magnitdue of momentum (length of vector).
A: There is nothing wrong with the quote because it assumes that the only allowed (or considered) motion is to the left or to the right. So the text is explaining things in the context of mechanics with one spatial dimension. And one-dimensional vectors are isomorphic to ordinary numbers. Their first and only component may be positive or negative, so one may also talk about positive and negative vectors.
Of course, this is not possible for higher-dimensional vectors. For at least 2-dimensional vectors, one has to talk about components with respect to specific axes if he wants to discuss the "signs of the momentum".
A: In some sense you're right when you say "the direction should be specified separately to the number". However you have to be careful about what you mean--if you say this then by 'number' you mean an unsigned quantity (think absolute value). When you start talking about the signs of numbers, either positive or negative, then that sign encodes information about the direction that something is moving. 
Note I have to define what 'positive' means and what 'negative' means, in the sense that positive doesn't always mean 'to the right'. It could mean 'to the left' as well. However once I make my choice I've set the meaning of positive and negative, and from then on 'positive' vectors point in that specific direction.
