Confirmation of cross products

  • Thread starter DeadOriginal
  • Start date
  • Tags
    Cross
In summary, cross products are a mathematical operation used to calculate the vector product of two vectors, resulting in a perpendicular vector. The accuracy of cross products can be confirmed using properties and calculations. In science, cross products have applications in physics, engineering, and computer graphics. If the cross product of two vectors is zero, it indicates parallel vectors or one vector being the zero vector. Cross products can be calculated in any dimension, but the resulting vector may only have a physical interpretation in three dimensions.
  • #1
DeadOriginal
274
2
I know that for the tangent unit vector ##t##, normal unit vector ##n##, and binormal unit vector ##b## that ##b=t\times n## and ##n=b\times t##. Is it true that ##t=n\times b##?

**Edit** Ah! Yes it is. Nevermind. I should have known this was true.
 
Last edited:
Physics news on Phys.org
  • #2
The trick is to prove it though ;)
 

What is the concept of cross products?

Cross products refer to a mathematical operation that is used to calculate the vector product of two vectors. It involves the use of the cross product formula and results in a vector that is perpendicular to the two original vectors.

How do you confirm the accuracy of cross products?

To confirm the accuracy of cross products, you can use the properties of cross products, such as the distributive property and the fact that the cross product of two parallel vectors is equal to the zero vector. You can also use geometric reasoning and mathematical calculations to verify the results.

What are the applications of cross products in science?

Cross products have various applications in science, including physics, engineering, and computer graphics. They are used to calculate torque, determine the direction of magnetic fields, and create 3D models and simulations.

What happens when the cross product of two vectors is zero?

If the cross product of two vectors is zero, it means that the two vectors are either parallel or one of the vectors is the zero vector. This can also mean that the two vectors are perpendicular, but one of them has a magnitude of zero.

Can cross products be calculated in any dimension?

Yes, cross products can be calculated in any dimension, but the resulting vector will only be perpendicular to the two original vectors if the dimension is three. In higher dimensions, the cross product will still be calculated, but the resulting vector may not have a physical interpretation.

Similar threads

Replies
4
Views
1K
  • Differential Geometry
Replies
2
Views
511
Replies
3
Views
1K
  • Differential Geometry
Replies
15
Views
3K
Replies
8
Views
2K
Replies
4
Views
1K
  • Differential Geometry
Replies
3
Views
2K
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Differential Geometry
Replies
6
Views
1K
Back
Top