How can I solve a 3D coordinate problem involving rotation and a given point?

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In summary, a person is seeking help in solving a problem involving a point and a line in 3D space. They are unsure of how to approach the problem and are wondering if anyone has any suggestions or if there is enough information given to solve it. Another person in the conversation questions the given statement and suggests a correction.
  • #1
pimanian
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I have been thinking about this problem for awhile, but have no idea to even begin solving it. Was wondering if anyone has a clue to help me started?
There's a point (x0,y0,z0) in 3D. There is a line on the X-Y plane. This line is say theta degrees (0 - 360) about the Y-axxis. If the point (x0, y0, z0) is rotated phi degrees about this line, what is the new position?
This is just a problem I thought up, so I don't even know if there is enough information to solve it.
Please help me, let me know what's a good step to solve it? Should I use Cartesian system, or use another one?
Thanks!
 
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  • #2
There are 'infinity' of lines that form the same angle with the y-axis. So if the exact line's not given, I don't think this is solvable.
Anyway, are you sure this statement is correct?
pimanian said:
say theta degrees (0 - 360)
Shouldn't that be 0 <= theta <= 90?
Viet Dao,
 
  • #3


To begin solving this problem, you can start by visualizing the given point (x0,y0,z0) and the line on the X-Y plane. Then, try to imagine how the point would move if it were rotated phi degrees about the line. This will help you understand the problem better and come up with a plan to solve it.
Next, it would be helpful to use a coordinate system, such as Cartesian coordinates, to represent the point and the line. This will make it easier to calculate the new position of the point after rotation.
You can then use trigonometry and geometry principles to determine the new coordinates of the point after rotation. Remember to consider the angle theta and phi when calculating the new position.
If you are still struggling, you can try breaking down the problem into smaller steps and tackling them one at a time. Also, don't hesitate to ask for clarification or further assistance if needed. Good luck!
 

FAQ: How can I solve a 3D coordinate problem involving rotation and a given point?

What is a coordinate problem?

A coordinate problem is a mathematical issue that involves finding the location of a point on a plane or in space using a set of coordinates. It can also refer to difficulties in understanding or interpreting coordinate systems.

What are the different types of coordinate systems?

The most commonly used coordinate systems are Cartesian coordinates (x, y), polar coordinates (r, θ), and spherical coordinates (r, θ, φ). Other coordinate systems include cylindrical coordinates, geographic coordinates, and galactic coordinates.

How do I solve a coordinate problem?

To solve a coordinate problem, you must first determine the type of coordinate system being used. Then, use the given information and any relevant formulas to find the coordinates of the point in question. Finally, check your solution to ensure it is accurate.

What are some common mistakes made when working with coordinates?

Common mistakes when working with coordinates include mixing up the order of the coordinates, using the wrong formula or coordinate system, and not accounting for negative values. It is important to double-check your work and be familiar with the specific coordinate system being used.

How can I improve my understanding of coordinates?

To improve your understanding of coordinates, it can be helpful to practice working with different types of coordinate systems and to familiarize yourself with common formulas and conversions. You can also seek out resources such as textbooks, online tutorials, or working with a tutor or mentor.

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