Why is the right hand rule for cross product?

Click For Summary
SUMMARY

The right-hand rule is a convention used to determine the direction of the cross product in a three-dimensional space, specifically within a right-hand coordinate system. The magnitude of the cross product indicates the area or volume enclosed by two or three vectors, while the direction is perpendicular to the plane formed by these vectors. This convention aligns with the standard naming of the axes (x, y, z) and ensures consistency in vector calculations. Adopting the left-hand rule would yield the same results but in the opposite direction.

PREREQUISITES
  • Understanding of vector mathematics
  • Familiarity with cross product operations
  • Knowledge of three-dimensional coordinate systems
  • Basic grasp of vector magnitude and direction
NEXT STEPS
  • Study the properties of vector cross products in detail
  • Explore the implications of using the left-hand rule in vector calculations
  • Learn about applications of the right-hand rule in physics and engineering
  • Investigate the relationship between cross products and torque in mechanics
USEFUL FOR

Students of physics and mathematics, engineers working with vector analysis, and anyone interested in understanding the conventions of three-dimensional vector operations.

iScience
Messages
466
Reaction score
5
so, the magnitude of the cross product represents the area or volume enclosed by any 2 or 3 vectors respectively, but what does the direction represent? i get that the general direction is one that is perpendicular to all the vectors, but what does the actual direction represent? ie, why the right hand rule? ie, why this particular direction instead of the opposite? is it just by convention or is there a particular reason?
 
Physics news on Phys.org
The right hand rule is just a convention. If one adopts the left hand rule everything would work the same only backwards. This is to fit with the usual naming of the axes x,y,z.
 
  • Like
Likes   Reactions: 1 person
To expand on what lurflurf said, it is just a convention. The coordinate system most widely used is a right-hand coordinate system. You can see for yourself by using the right-hand rule on the x and y axes.

This would lead to the z-axis point towards you if the y-axis is oriented vertically and the x-axis oriented horizontally (in the plane perpendicular to your vision).

The right-hand rule just makes all the cross products you perform in this space conform to this.
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
Replies
21
Views
4K
  • · Replies 11 ·
Replies
11
Views
17K
  • · Replies 14 ·
Replies
14
Views
4K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 26 ·
Replies
26
Views
18K
  • · Replies 16 ·
Replies
16
Views
5K
  • · Replies 32 ·
2
Replies
32
Views
4K
  • · Replies 6 ·
Replies
6
Views
3K