Cross Product: Right-Hand Rule Explained

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SUMMARY

The discussion clarifies that in vector mathematics, the cross product of two vectors, represented as vectorA × vectorB, is equal to the negative of the cross product of the vectors in reverse order, expressed as vectorB × vectorA = - (vectorA × vectorB). This relationship is explained through the right-hand rule, which indicates the direction of the resultant vector. When vectorA is rotated towards vectorB, the right-hand rule points upwards, while rotating vectorB towards vectorA results in a downward direction, confirming the anti-commutative property of the cross product.

PREREQUISITES
  • Understanding of vector operations
  • Familiarity with the right-hand rule in vector mathematics
  • Basic knowledge of cross product properties
  • Ability to visualize vector rotations in three-dimensional space
NEXT STEPS
  • Study the properties of vector cross products in detail
  • Learn about the right-hand rule and its applications in physics
  • Explore vector rotation techniques in three-dimensional geometry
  • Investigate the implications of anti-commutativity in vector calculus
USEFUL FOR

Students of physics, mathematicians, and anyone studying vector calculus or three-dimensional geometry will benefit from this discussion.

hilarious
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In the cross product, why is vectorA*B=-(vectorB*A)
How does the right-hand rule apply to this formula?
 
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Look at the picture. If you rotate A towards B, the right-hand rule points upwards. If you rotate B towards A, the fingers point the opposite way, so the right-hand rule points downwards.
 
hilarious said:
In the cross product, why is vectorA*B=-(vectorB*A)
Apply the definition of cross product

hilarious said:
How does the right-hand rule apply to this formula?
265px-Right_hand_rule_cross_product.svg.png

What happens to the direction of a x b when you rotate the hand to swap the directions of a and b ?
 

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