They're both negatives of the other. (That is, add the two vectors together and you end up with 0.) They're just not negative in the sense of being "less than zero."

So taking the negative of 2i + 6j gives you -2i - 6j.
Likewise, taking the negative of -2i -6j gives you 2i + 6j.

 

here's a quick mental test as to whether negative volume exists:

a normal, everyday cup has positive volume. pour water into it, and it starts to fill up, until it's entire volume is filled and can accept no more.

now, think of something wherein the more water you pour into it, the more it can hold without changing it's shape. the more liquid you add, the more it can hold, until it can hold an infinite amount of liquid.

black hole? that's theoretical physics way beyond my scope.

but, exist in our everyday reality. nope.

ok, thread over.

 

[QUOTE=Elistan,Dec 6 2005, 07:07 AM]They're both negatives of the other.

 

Yes, sorry, I wasn't clear. dcak is indeed incorrect in that you cannot point to any particular vector and say "that one is negative." I was trying to explain to him what the term "negative" means in regards to vectors. My apologies if I came off as trying to contradict you.

 

There's no such thing as a negative vector. There are negatives of other vectors, but nothing that says a certain vector is absolutely negative.

It is a area/volume/whatever, but signed!

That's okay, you've got us to worry about the math for you

 

This reminds me of a joke:

A researcher is trying to determine the differences in the thought processes of mathematicians, philosophers, physicists, and engineers. They are each given the hypothesis, "All odd numbers greater than 1 are prime" and told to prove or disprove it.

The mathematician says, "Three is a prime, five is a prime, seven is a prime, nine is not. Clearly, the hypothesis is false."

The philosopher says, "Three is a prime, five is a prime, seven is a prime. Clearly, by induction, the hypothesis is true."

The physicist says, "Three is a prime, five is a prime, seven is a prime, nine is not, eleven is a prime, thirteen is a prime. Clearly, the hypothesis is true; nine is just 'experimental error'."

The engineer says, "Three is a prime, five is a prime, seven is a prime, nine is a prime, eleven is a prime, thirteen is a prime, . . . ."

 

 

"Darwinist"

3, 5, and 7 are prime. 9 is not.

11, and 13 prime. 15 is not.

Clearly the prime numbers are evolving into non-primes, as these non-primes are more suited to their "odd" environment.

(Aside: 9 looks similar to the 6... neither of which are prime. 9 and 6 likely share a common ancestor.)

---

Kansas Board of Education:

The 3 doesn't look anything like the 5, and the 7 looks like an upside down L. And amazingly, all are prime! The complexities are simply wonderous! To think anything different would surely be blasphemous.

Clearly, we should allow for the possibility that a higher power-- through some form of intelligent design-- has created all the numbers, both prime and non-prime. Amen... *cough* I mean... or so it is hyptothesized.

 

very interesting... gets you thinking