Question

Can someone help me with this please.

A vector field in cylindrical polar co-ordinates is given by
V = R Rˆ + R 3 s i n ( φ ) c o s ( φ ) φˆ + 3 z kˆ

where Rˆ, φˆ, kˆ are the appropriate unit vectors. Translate this vector field into the
Cartesian x, y, z co-ordinate system.

What is the first step??

Could you please guide me through the steps.
Thanks.

I get that
x = r cosφ
y = r sinφ
z = z

And i know i need to sub 'unit R^' with cosφ i + sinφ j and z with 'unit K^' with z k.

How about 'unit φ^' ?
What do i need to sub phi with?
I look else where it says sub it with -sinφ i + cosφ j.
But how? and why?
Can someone explain it to me?

Thanks alot!

Answer 1

In your previous post, you have been asked what R3 stands for, and you have not clarified. We do not know yet if 3 is a superscript, a subscript, or just a number written in the wrong place.
Yes, <b>φ</b> equals a vector
< -sinφ, cosφ, 0 >.
Also, are
R,φ and z constants?
How is <b>k</b> related to <b>z</b>, there must exist a multiplicative constant, unless the constant equals 1.

Answer 2

Take a look at your previous post. See whether my solution makes any sense, and whether I interpreted things correctly.