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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?
How does the right-hand rule apply to this formula?
Cross Product: Right-Hand Rule Explained
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In summary, the cross product formula for vector A*B is equal to the negative of vector B*A. This is because the right-hand rule dictates that when rotating vector A towards vector B, the right-hand rule points upwards, but when rotating vector B towards vector A, the right-hand rule points downwards. This is also consistent with the definition of cross product, where the direction of the resulting vector is determined by the right-hand rule.
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Svein
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A.T.
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Apply the definition of cross producthilarious said:
hilarious said:
What happens to the direction of a x b when you rotate the hand to swap the directions of a and b ?
What is the cross product?
The cross product, also known as the vector product, is a mathematical operation between two vectors that results in a third vector. It is used to determine the direction and magnitude of a vector perpendicular to the two original vectors.
How is the cross product calculated?
The cross product is calculated using the right-hand rule, which involves taking the first vector in your right hand, pointing your fingers in the direction of the second vector, and then curling your fingers towards the first vector. The direction of the resulting vector will be perpendicular to both original vectors.
Why is the right-hand rule used for the cross product?
The right-hand rule is used for the cross product because it is a convention that helps us determine the direction of the resulting vector in a consistent and intuitive way. It also allows us to visualize the vector in 3D space.
What is the significance of the direction of the cross product?
The direction of the cross product is significant because it tells us the orientation of the resulting vector in relation to the two original vectors. This is important in many applications, such as determining torque in physics and the direction of rotation in engineering.
Can the cross product be used in 2D space?
No, the cross product can only be calculated in 3D space. In 2D space, the cross product would result in a vector with a magnitude of 0, as there is no perpendicular direction to the two original vectors.
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