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I was given this problem on a test:

a vector A = 2yi- Zj+3xk, was given in rectangular (cartesian) coordinates and I had to convert it to cylindrical coords. What I did to solve it was this:

1) A = 2rsin(theta)i- zj+ 3rcos(theta)k

2) partial derivatives

a) d/dr = 2sin(theta)i+ 3cos(theta)j

b) d/d(theta) = 2rcos(theta)i- 3rsin(theta)k

c) z = k = 3rcos(theta)k

3) dot product (initial vector A with each of the partial derivatives)

a)*A =4rsin^2(theta) + 9rcos^2(theta) = r

b)*A = 4(r^2)sin(theta)cos(theta) - 9(r^2)cos(theta)sin(theta) =-5(r^2)sin(theta)cos(theta) = theta

c)Z = K = 3rcos(theta)

the equations in bold are my final answers. I would appreciate any feedback on what I did (if it is right or wrong). Many thanks!

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# Rectangular to cylindrical conversion

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