# Vector Transformations

1. Feb 20, 2006

### Living_Dog

Problem 1.10(a) of DJGriffiths asks: "How do the components of a vector transform under a translation of coordinates?"

This is confusing me (not hard to do) since the translation is given, then isn't it just:

x' = x + A

where A = $$\left(\begin{array}{c} 0 \\ -a \\ 0 \end{array}\right)$$

Problem 1.10(b): The same "... inversion ..." so that x' = -I x?

Problem 1.10(c): "How does the cross-product of two vectors transform under inversion?"

Once again, if A is a vector, then it transforms as always A' = RA.

So how is it any different if the vector is generated by a cross-product or is made up by me? It's a vector! Unless the question is not asking about A', but rather about how does BxC transform??? ...how would I apply the ransformation to the actual cross-product? I mean, do I take RBxRC or R(BxC)??

sorry if my questions are annoying or too frequent. but it's always the same thing - I read the chapter and have no problem following the theory. Then I get to the Problems section and suddenly it's like the questions have nothing to do with the chapter I just read!

-LD

Last edited: Feb 20, 2006
2. Feb 20, 2006

### Tom Mattson

Staff Emeritus
No, vectors are invariant under translation. For instance if you and I are at rest relative to each other but standing at different locations, and one of us observes a car zipping by at 50 mph due east, then the other of us will agree with that velocity measurement.