Cross product in non-cartesian coordinates?

Click For Summary
SUMMARY

The discussion focuses on calculating the cross product of two vectors in cylindrical coordinates, specifically one vector aligned with the radial direction (R) and another with the angular direction (theta). It is established that the cross product can indeed be computed regardless of the coordinate system, provided the vectors are represented in terms of their perpendicular components. The magnitude of the cross product is determined by the product of the magnitudes of the two vectors when they are perpendicular.

PREREQUISITES
  • Understanding of cylindrical coordinates
  • Knowledge of vector operations, specifically cross products
  • Familiarity with vector representation in different coordinate systems
  • Basic trigonometry to understand angles between vectors
NEXT STEPS
  • Study the mathematical formulation of the cross product in cylindrical coordinates
  • Learn about vector representation in different coordinate systems, including Cartesian and spherical
  • Explore the properties of cross products and their geometric interpretations
  • Investigate applications of cross products in physics, such as torque and angular momentum
USEFUL FOR

Students and professionals in physics, engineering, and mathematics who need to understand vector operations in non-Cartesian coordinate systems, particularly those working with cylindrical coordinates.

moonman
Messages
21
Reaction score
0
How do you go about crossing two vectors if they are in cylindrical coordinates? I have one vector in the direction of R and another in the direction of theta. Can this be done?
 
Physics news on Phys.org
moonman said:
How do you go about crossing two vectors if they are in cylindrical coordinates? I have one vector in the direction of R and another in the direction of theta. Can this be done?

Two vectors (non-parallel) lie in a plane. The cross product is always a vector perpendiculat to that plane. When the two original vectors are perpendicular, the magnitude of the cross product is the product of the magnitutes. The basis for representing the vectors does not change this. As long as you represent the vectors in terms of perpendicular components, or if you know the angle between them, the cross product can be determined.
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
998
  • · Replies 5 ·
Replies
5
Views
2K
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
924
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K