What is i,j,k in the 3D coordinate system?

Question

Im starting to study about the theory of relativity and I have a Q about the 3D coordinate system. I know that I have x, y an z and that the vectors i,j,k are related to them but what do they represent,why do we need them and what is the use of i,j,k vectors?

Answer 1

The î, ĵ, k are unitary vectors.



Unitary vectors are ones with module (norm or length) equals one. The 3d coordinate system can be constructed with 3 linearly independent unitary vectors, called basis of the system. Also is possible to construct 3d systems with non-unitary vectors. Any other vector in the 3D space is constructed as a linear combination of the basis vectors. The basis vectors must be linearly independent. It means that:



aî+bĵ+ck /= 0



for all real numbers a,b,c. The î, ĵ, k basis is an orthonormal basis, meaning that the basis vectors are unitary and orthogonal with each other. A non-orthonormal basis is one in wich the basis vectors aren't unitary or orthogonal.



:)

Answer 2

i means x

j means y

k means z



these are basically used to represent directions

when u put a ^ over i/j/k it represents a vector of unit magnitude in that particular direction



like its written (3i^ + 4j +6k)

it represents that there are three vectors of magnitude 3,4,6 in x,y,z directions resp.

the reaultant vector has a magnitude of square root of ( 3^2 + 4^2 + 6^2) = square root of 61

Answer 3

i,j,k are the names of three more Cartesian system co-ordinates, so a line from x to i describes that vector and so on.



sometimes they are the shifted locations of x,y,z after some sort of transformation so if for example you rotate space 90 degrees around the x axis, i.j.k. point comes towards you out of the paper, as it were, meaning the original point has relatively to you, moved

Answer 4

suppose you are given a vector in the x-y plane.. assume it to be force vestor of magnitude 50N at a particular angle.. lets assume 30 degree.. you break it into two componets.. one in the drctn of x axis and other in 3 axis.. ie.. 50sin30 and 50cos30.. now to simplfy it.. we simply write 50i and 50j..

i hope ur gettin my point..

i mean.. if yu were not to be given i and j.. ude simply be wring x or y.. i j k are just for showing the reader where the frekkin vector is going! :P

Answer 5

Here is the history of quaternions:

http://en.wikipedia.org/wiki/Quaternion