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"

 

[thomate1]

I understand your confusion and I would like to clarify the correct answer for this vector conversion problem in cylindrical coordinates.

Firstly, let's review the correct conversion process. In cylindrical coordinates, the position vector is expressed as r = row(cos(fie), sin(fie), z).

In this problem, we are given the coordinates (5,2,3). Using the formula for row, we get row = SQRT(5^2 + 2^2) = 5.385.

Next, we need to find the value of fie. To do this, we use the formula tan(fie) = y/x. Plugging in the values of y and x, we get tan(fie) = 2/5. Taking the inverse tangent, we get fie = tan-1(2/5) = 21.8 degrees.

Finally, we can express the position vector in cylindrical coordinates as r = 5.385(cos(21.8), sin(21.8), 3).

Now, let's look at the answer choices.

A) This answer is incorrect as it uses spherical coordinates instead of cylindrical coordinates.

B) This answer is incorrect as it does not include the correct value of fie.

C) This answer is correct as it correctly includes the values of row and z, and the correct value of fie.

Therefore, the correct answer is C.

I hope this explanation helps clear up any confusion and if you have any further questions, please do not hesitate to ask your professor for clarification. As scientists, it is important to understand and accurately apply mathematical concepts. Good luck with your studies!