Question

I need a confirmation. Do I just sketch and label or is there a more complicated way to show this? (picture)

Answer 1

I think, assuming e_1, e_2 and e_3 are the canonical cartesian basis, you must express the cylindrical position vector in cartesians. So you must calculate. Also I think is as @Jemurray3 says, but you must know the expression of the scalar product of the unitary vectors in the right side.

Answer 2

Well, also it should be easier to sketch it.

Answer 3

I would just draw it.

Answer 4

^ Made a mistake in the above, so I am editing:

If you want to be explicit, recognize that in the x-y plane,

\[ \hat r \cdot \hat x = \cos(\phi)\]
\[\hat r \cdot \hat y = \sin(\phi) \]
So the vector in x-y plane could be expressed as
\[ \vec{r} = r\cos(\phi) \hat x + r\sin(\phi) \hat y\]

Answer 5

So I sketched it. Is it right that I wrote:

Magnitude along x-axis = r cos (phi)
y-axis = r sin (phi)
z-axis = z

And then wrote:

So the position vector in cylindrical will be the magnitude dotted with the unit vectors for cylindrical coordinates.

Answer 6

You don't need that last bit -- the vector is equal to the projection of the vector onto each axis times the corresponding basis vector.

Answer 7

Alright thanks!