addition and subtraction of vectors

[Mao]

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.

hehe, by your definition, arithmetics isnt a field either:



subtractions dont need to be commutative. it is defined as the addition of the additive inverse, that is:

let a, b be two vectors:

[enpassant]

There is no such thing as a position vector plus another position vector, and it is not equal to a third position vector. Suppose in your example the displacement (a free vector) has the same magnitude and direction as b (the second position vector), then a + displacement = the third position vector.

[dcc]

I put forward an example such as:

The position vector for walking 1 kilometer east of the shops at (0,0) is
The position vector for walking 1 kilometer north of the shops (to where my house is) is
The position vector for walking 1 kilometer east of my house is

clearly you can add position vectors in a real life situation

[evaporade]

The first two are displacement vectors, not position vectors. I think you are confused with position and displacement vectors.

[Mao]

The first two are displacement vectors, not position vectors. I think you are confused with position and displacement vectors.

i'm sorry, the use for being this pedantic is?

a position vector can be just as easily used as a displacement vector.

(and when you think about it, a position vector is expressed in terms of i, j and k, which are unit vectors perpendicular to each other, so by definition, position vectors are actually displacement vectors from O)

[evaporade]

Displacement = final position - initial position. If the initial position is the origin, then displacement = final position, it means the displacement vector has the same magnitude and direction as the final position vector; it does not mean the displacement vector and the final position vector are the same. A position vector tells you the location of a point relative to the origin. It is an arrow always starting from O and .: it is not a free vector. Displacement is a free vector, it tells the straight line distance and direction of a change in position.

[dcc]

to be honest, i disagree completely with what you are saying

evidence:
http://en.wikipedia.org/wiki/Displacement_(vector)

In physics, displacement is the vector that specifies the position of a point or a particle in reference to an origin or to a previous position. The vector directs from the reference point to the current position.

When the reference point is the origin of the chosen coordinate system, the displacement vector is better referred to as the position vector..

All these vectors start from the origin (indicated by the O), and are thus position vectors, rather then displacement vectors.

Also, if we were to write these out mathematically (using i as east, j as north), then you are saying



i fail to see the distinction that you can make between the three vectors, they all start the the origin (and remembering our vectors knowledge, vectors which start from a fixed inertial point of reference (i.e. origin) are called POSITION vectors)

[evaporade]

walking 1 kilometer east of the shops at (0,0), your displacement is 1 km east, your position is 1 km east of (0,0), a further displacement of 1 km north of your new position (i.e. 1 km east of (0,0) ), your total displacement is sqrt2 km NE, and your final position is sqrt2 km NE of (0,0). So you are adding displacement to position vector, not position vector to position vector.

You cannot be 1 km east of (0,0) and 1 km north of (0,0) at the same time, and then add the two positions and say your final position is sqrt2 km NE of (0,0).

[Mao]

erm guess what guys???

http://vcenotes.com/forum/index.php/topic,2102.0.html

i suggest you take a read (yes, "you" as in singular, e------t cetera)

oh, and erm...
perhaps dcc didnt say it clearly (or you just need a repeat):

evidence:
http://en.wikipedia.org/wiki/Displacement_(vector)

In physics, displacement is the vector that specifies the position of a point or a particle in reference to an origin or to a previous position. The vector directs from the reference point to the current position.

When the reference point is the origin of the chosen coordinate system, the displacement vector is better referred to as the position vector..

All these vectors start from the origin (indicated by the O), and are thus position vectors, rather then displacement vectors.

...

i fail to see the distinction that you can make between the three vectors, they all start the the origin (and remembering our vectors knowledge, vectors which start from a fixed inertial point of reference (i.e. origin) are called POSITION vectors)

perhaps you shall now argue about why a square is different to a quadrilateral, and that 0.999999999999(repeat) is different to 1.

[Toothpaste]

"bwahaha".

[dcc]

are you saying that for displacement to occur, i must only walk in straight lines from my chosen point of origin? saying that i 'cannot be in the same place at two times' is like saying that 'i cant have an infinitely small thing therefore calculus doesn't exist'

lets take this simple example:







could i not alternatively define the position vector as the sum of the position vectors and ?

have you ever seen how vector addition works graphically? i would suggest reading up on the concepts involved.

[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.

hehe, by your definition, arithmetics isnt a field either:

Hahaha, ooops. I was just trying to be a smart arse

[evaporade]

whether you walk in a straight line or along a curve, if your final is 1km east of your initial, your displacement is 1 km east.

when you add vectors you move the tail of one to the head of the other. you can't do this with position vectors because you can't move them, they always start from O

[evaporade]

A displacement vector from O to certain point can be considered as a position vector, but a position vector is not a displacement vector.

[evaporade]

saying that i 'cannot be in the same place at two times'
Please read post carefully.