addition and subtraction of vectors

[enpassant]

the locations of points A and B are a = 2i - 3j and b =-i -j respectively, find and interpret a - b and a + b if exist.

[Mao]

i'd presume so, they are both on the i-j plane:

[evaporade]

I doubt your presumption is correct.

[Mao]

I doubt your presumption is correct.

how so?
i dont see how its false....

[Captain]

I doubt your presumption is correct.

Mao is definatly right....

Only thing that is technecally not right is you can't subtract vectors.  You have to add the negative vector.

a + -b
2i-3j + -(-i-j) = 2i-3j+i+j = 3i-2j

Same thing...Just what my teacher says

[Mao]

Only thing that is technecally not right is you can't subtract vectors.  You have to add the negative vector.

hehe

but i thought the definition of subtraction of a number is the addition of the number's additive inverse
thats how they define it in a "field" anyways

and same goes for division by a number is the multiplication of the numbers's multiplicative inverse

captain you will have it in your MUEP notes from week 1


so in a way we're talking about the same thing
except ur more of a purist lol

[Captain]

Only thing that is technecally not right is you can't subtract vectors.  You have to add the negative vector.

hehe

but i thought the definition of subtraction of a number is the addition of the number's additive inverse
thats how they define it in a "field" anyways

and same goes for division by a number is the multiplication of the numbers's multiplicative inverse

captain you will have it in your MUEP notes from week 1


so in a way we're talking about the same thing
except ur more of a purist lol

Mao, you are correct.  However that sort of depth isn't required for the Specialist Math's syllabus, IIRC.

[cara.mel]

Only thing that is technecally not right is you can't subtract vectors.  You have to add the negative vector.

hehe

but i thought the definition of subtraction of a number is the addition of the number's additive inverse
thats how they define it in a "field" anyways

and same goes for division by a number is the multiplication of the numbers's multiplicative inverse

captain you will have it in your MUEP notes from week 1


so in a way we're talking about the same thing
except ur more of a purist lol

Is that for vectors or for all numbers? =/

[Mao]

Is that for vectors or for all numbers? =/

pretty much for ALL of math xD

[cara.mel]

Dont laugh at me.

[evaporade]

a and b are position vectors. Subtraction of two position vectors gives displacement (change in position), but addition of two position vectors is undefined.

[Collin Li]

a and b are position vectors. Subtraction of two position vectors gives displacement (change in position), but addition of two position vectors is undefined.

Please provide a source for this.

[Captain]

but i thought the definition of subtraction of a number is the addition of the number's additive inverse
thats how they define it in a "field" anyways

Now I look at this again, I don't think vectors have the same rules applied as a field.

Vector subtraction is not commutative.  Which IIRC is a requirement of a field.

a and b are position vectors. Subtraction of two position vectors gives displacement (change in position), but addition of two position vectors is undefined.

Since when has addition of vectors been undefined? I just did a quick google for an example.

[evaporade]

Addition of free vectors is defined, but the addition of position vectors (they are not free vectors) is undefined. Position vectors must all start from a reference point, the origin O, and you don't put them head to tail (they are not free vectors) as done in addition of vectors. Ask yourself this question: a - b means displacement, what is the meaning of a + b?

[Mao]

Addition of free vectors is defined, but the addition of position vectors (they are not free vectors) is undefined. Position vectors must all start from a reference point, the origin O, and you don't put them head to tail (they are not free vectors) as done in addition of vectors. Ask yourself this question: a - b means displacement, what is the meaning of a + b?

here's one:
A square in 2D has vertices at O, A (position vector a), and B (position vector b). a-b in this case is displacement (), a+b is the position vector for the other corner.