Convert the coordiates of one vector between 2 Cartesian system

[bigworld005]

hi, all,
run into one geometry problem: I have two 3-D Cartesian systems, A and B. they share the same original. the coordinate (2,3,3) in B system is the same vector as (118,2090,1000)in A system( there may be scale difference, but they are the same direction); then what is the vector in B corresponding to (89,2600,1000) in A?
I know there should a standard formula for this kind of conversion. but I didn't take this class, would anyone recommend any book on this? is there a software doing this work?

thanks,
t

 

[llarsen]

You haven't given enough information to answer your question. Two vectors can be mapped to each other in many ways. There isn't enough context to tell whether coordinate system A and coordinate system B have a metric which would narrow things down a bit. Knowing the type of units associated with the coordinate systems would be useful (for example - inches, seconds, degrees farenheit). Even that this not enough to uniquely identify the two coordinate systems, but it starts to narrow things down.

 

[bigworld005]

hi,
thanks for the reply. what I mean is very simple: in the space where we live, I have two Cartesian coordinate sharing the same origin, the direction in system A is (118,2090,1000), while in B is (2,3,3); then the direction (89,2600,1000) in A correspond to which direction in B?
this time, using the word of "direction" instead of "vector" may help.

 

[bigworld005]

Hi,
I forget to mention: the scale in the two system is same, so no shrink or extend in the axis.
by the way, I think Cartesian system means the three axises X,Y,Z, they are normal to each other. hope I am right.

thanks,
t