Question

Why do we need a seprate branch of mathematics in order to deal with vectors.How would you diff b/w Vector Algebra and Vector Calculus.

Answer 1

@experimentX

Answer 2

what have you done so far?

Answer 3

Well i just went took the first lecture and i know that Both of these(i.e Vector algebra and Vector Calculus) act as tools for handling vector quantities.

Answer 4

calculus deals with changes ... and you have functions for changes. A function can be vector valued. that's all.

Answer 5

Why do we need a seprate branch of maths?

Answer 6

To deal with Vectors?

Answer 7

One more thing that What do we need in order to Specify an abstract quantity?

Answer 8

Because it is not Completely measurable.

Answer 9

abstract quantity is generalization of all.

Answer 10

there are lots of things which have common stuff ... so we define abstract quantity (with basic set of rules) so it includes all those quantities.

Answer 11

Can you base your dicussion with a certain example?

Answer 12

first you define a vector space ... now think of what can be included in vector space.

Answer 13

you have bunch of stuff like ... vectors, matrices, space on coefficient of polynomials ... etc etc, now they all follow same set of rules which a vector space follows. It makes thing much easier.

Answer 14

Thanks.

Answer 15

also there are lot's of examples ... particularly on a branch of mathematics called abstract algebra ... But i know too little on it.

Answer 16

One more discussion which i put forward was that if time moves in a particular direction from past to future.Is it a vector?

I got a response that if time was a vector it should also follow the Vector laws.

But if that was the case wouldn't space time would also be a Scalar?

Answer 17

what are the vector laws??

Answer 18

Vectors law of addition,Multiplication with a number (scalar multiplication) and of the vector (Dot and Cross Product).

Answer 19

cross product is only valid for 3 d ..

Answer 20

and you have a distance formula in space time ... it's called geodesic. that should be similar to the scalar product.

Answer 21

Well it should follow the vector laws of addition an sub.

Answer 22

it should ... since space time is a vector space.

Answer 23

If we Becuase you think of it as dimension... how ever it is wrong... space time is not a vector quantity either.

Answer 24

how do you say that?

Answer 25

Current is a scalar or a vector quantity?

Answer 26

current is scalar.

Answer 27

Well current also moves in a particular direction but it does not follow the vectors law of addition and subtraction therefore it is scalar.

So keeping this as a base I say time and space time are also scalars.


If you would have done the dimensional analysis you would know.

Answer 28

I haven't done dimensional analysis. and I actually don't know if space time is a vector or not. So far, I can tell space time is a vector space.

Answer 29

Hmm :/

Anyways,Thanks a lot for helping :)

Answer 30

you are welcome

Answer 31

About current ... actually I never have thought this before. current is a quantity that flows in 1 dimensional space. In 3d space, this is definitely not a vector.

Answer 32

Dimensional analysis is something important.

Btw,Current is not a Vector.

Answer 33

do you mean this
http://en.wikipedia.org/wiki/Dimensional_analysis
I did this long before on High School.

Answer 34

Yes,I also did it in high school.

Answer 35

i think you cannot define 3d space as vector itself. An element of vector space can be scalar or vector.

Answer 36

I am sorry i gotta go,I have a class now.Bye.

I would look into that when I come back.Thanks a lot,you were very helpful.