Solve Vector Conversion Problem in Cylindrical Coords

[bengaltiger14]

Homework Statement

I had an exam conversion problem:

A position vector (between the origin and point (5,2,3) is expressed as r = 5x+2y+3z. Express this vector in cylindrical coordinates.

row = SQRT(5^2 + 2^2) = 5.385

Fie = tan-1(2/5) = 21.8 degrees

Z = Z.

This was a multiple choice test and the answers were:

A) r=2.232r+0.134(theta)+3(fie)
B) r=0.5(row)-0.866(fie)+3z
C) r=5.385(row)+3z
D) None of the above

I chose D, because the correct value of fie is not there and A is sypherical.. But, I got it wrong and the correct answer is said to be C.

I wanted to check with you guys first before going to the professor but is there something I missed??

 

[CompuChip]

You could argue that when setting up the coordinates you have the freedom to choose $\phi = 0$ at that point, although I agree that it is rather unusual... normally one takes $\phi = 0$ for points on the x-axis. If you are not sure however, I suggest you go see your professor anyway; the least he can do is explain why the answer should be C and why he thinks you are wrong.

By the way, $\rho$ is called "rho" and $\phi$ is "phi", just like $\pi$ is spelled "pi" instead of "pie"