If you have a transform
then
where
In this case we have
This gives us
I don't understand this problem. This is supposedly a review question from calc 3, but I've never seen anything like this before. Fortunately, I solved it, but I just don't understand what I did. (It's probably the weird notation I'm not used to.)
Express the r-component, , or a vector A at
(A) In terms of and in Cartesian coordinates, and
(B) in terms of and in spherical coordinates.
My book says:
"The vector in Cartesian coordinates with components can be written as:
Answers:
(A)
(B)
So for part (A), is that written in the same form as the unit vectors i hat, j hat, and k hat? And for part (B), why are both components divided by the radius?
It's a bit confusing to have the radial component be called r in both the cylindrical and spherical coordinates, so I'll use r=R in spherical coordinates.
To convert from one basis to another, you can use this little trick:
Not getting the same answer as you though...