How Is the Magnitude of the Cross Product Related to Parallelogram Area?

Click For Summary
SUMMARY

The magnitude of the cross product ||V x U|| is definitively equal to the area of the parallelogram formed by the vectors V and U. This relationship is established through geometric principles, where the area is calculated as the product of the base and height, with the cross product providing the necessary perpendicular vector. The proof involves demonstrating that the length of the cross product vector corresponds to the area of the parallelogram defined by the two vectors.

PREREQUISITES
  • Understanding of vector operations, specifically cross products.
  • Familiarity with geometric concepts related to area calculation.
  • Basic knowledge of linear algebra and vector spaces.
  • Proficiency in visualizing geometric shapes in a three-dimensional space.
NEXT STEPS
  • Study vector cross product properties in depth.
  • Explore geometric interpretations of vector operations.
  • Learn about applications of cross products in physics and engineering.
  • Investigate proofs related to vector areas and their geometric implications.
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are looking to deepen their understanding of vector operations and their geometric applications.

ƒ(x)
Messages
327
Reaction score
0
How do you prove that ||VxU|| is the area of the parallelegram they form?

I know that the cross product is a vector perpendicular to V and U
 
Physics news on Phys.org
Nvm, found a proof.
 

Similar threads

Replies
6
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
6
Views
8K
  • · Replies 19 ·
Replies
19
Views
2K
  • · Replies 13 ·
Replies
13
Views
4K
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K