# Solve Vector Conversion Problem in Cylindrical Coords

• bengaltiger14
In summary, the conversation discusses a conversion problem involving a position vector expressed in terms of cylindrical coordinates. The test was multiple choice and the correct answer was C, which was not chosen by the speaker. They question whether or not they missed something and consider asking their professor for clarification. The conversation also includes a side note about the proper spelling of certain symbols used in the problem.
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??

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"

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!

## 1. What are cylindrical coordinates and how are they used in vector conversion?

Cylindrical coordinates are a type of coordinate system that is commonly used in three-dimensional space. They consist of a radial distance, an angle in the xy-plane, and a height or z-coordinate. These coordinates are used to describe the position of a point in space and are particularly useful when working with cylindrical objects or surfaces. In vector conversion, cylindrical coordinates can be used to represent a vector in terms of magnitude and direction.

## 2. What is the process for converting a vector from Cartesian coordinates to cylindrical coordinates?

To convert a vector from Cartesian coordinates (x, y, z) to cylindrical coordinates (r, θ, z), you can use the following equations:

r = √(x² + y²)
θ = tan⁻¹(y/x)
z = z

Where r represents the radial distance, θ represents the angle in the xy-plane, and z represents the height or z-coordinate.

## 3. Can you explain how to solve a vector conversion problem in cylindrical coordinates?

To solve a vector conversion problem in cylindrical coordinates, you can follow these steps:

1. Determine the coordinates of the initial and final points in cylindrical coordinates.
2. Use the conversion equations to find the magnitude and direction of the vector in cylindrical coordinates.
3. To find the magnitude, use the Pythagorean theorem to calculate the radial distance and the height or z-coordinate.
4. To find the direction, use trigonometric functions to find the angle in the xy-plane.
5. Use the magnitude and direction to represent the vector in cylindrical coordinates.

## 4. Are there any limitations to using cylindrical coordinates for vector conversion?

While cylindrical coordinates are useful for representing vectors in certain situations, they do have some limitations. One limitation is that they are not always the most suitable coordinate system for a given problem. For example, if the vector lies in a plane parallel to the xy-plane, it may be easier to use polar coordinates instead. Additionally, cylindrical coordinates are not as commonly used as Cartesian coordinates, so it may take some time to get used to working with them.

## 5. How can I check my solution to a vector conversion problem in cylindrical coordinates?

To check your solution to a vector conversion problem in cylindrical coordinates, you can convert the vector back to Cartesian coordinates and see if it matches the original vector. You can also use algebraic techniques, such as vector addition and subtraction, to verify that the components of the converted vector are correct. Additionally, you can use software or online calculators to perform the conversion and compare the results.

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