How do you do vector addition in cylindrical coordinates?

[yungman]

My question is about vector addition in cylindrical coordinates:
Let A = 2x + y, B = x + 2y. In rectangular coordinates, AB = B-A = -x+y

In cylindrical coordinates, x=rcosθ + θsinθ, y=rsinθ + θcosθ
A =Axx + Ayy, B =Bxx + Byy

Ar = Ax(x.r) + Bx(y.r)=2.236, Aθ = 0. So A = 2.236r
Br = 2.236, Bθ = 0. So B = 2.236r

How do you do vector addition in cylindrical coordinates? A + B = 2.236r +2.236r !

Attached is the hand written file for clearer description.

I don't know how to add the two vectors totally in cylindrical coordinates because the angle information is not apparant. Please tell me what am I doing wrong.
Thanks

 

[tiny-tim]

Welcome to PF!

Hi yungman! Welcome to PF!

Why do you want to do this?

It doesn't seem to make any sense.

You're subtracting OA from OB to get AB.

OA and OB can be translated into cylindrical coordinates, because they start at O.

But AB doesn't … so how can AB have cylindrical coordinates?

 

[yungman]

Hi yungman! Welcome to PF!

Why do you want to do this?

It doesn't seem to make any sense.

You're subtracting OA from OB to get AB.

OA and OB can be translated into cylindrical coordinates, because they start at O.

But AB doesn't … so how can AB have cylindrical coordinates?

Thanks for the response, I am trying to learn vectors in other coordinates and I find it hard to buy a book with detail explanation.
This is just a very simple example of what I want to learn. I don't know how they can do simple addition of two vectors in curvilinear coordinates because the two points are at different reference position ( they have different θ in my case ) and it cannot be added like the vectors in rectanglar coordinates. I am still learning so I don't dare to make this conclusion, that is why I put it up here so others can give me an answer.

Is this kind of vector in curvilinear coordinate mainly use in vector field calculation where you can only do vector algebra in the same curvilinear plane( the curvilinear planes of same origin only)?

Thanks