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ChaoticLlama
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http://imgur.com/mceBq" [Broken]
I'm curious to see if my conclusion is correct.
thanks in advance.
I'm curious to see if my conclusion is correct.
thanks in advance.
Last edited by a moderator:
CompuChip said:I don't really agree with your claim that if for two vectors a (non-zero) and b, axb = 0, then b = 0.
Mark44 said:Following up with what CompuChip said, what is a X 2a?
A cross-product is a mathematical operation that takes two vectors as input and produces a third vector that is perpendicular to both of the original vectors. It is also known as the vector product or outer product.
The cross-product is calculated by taking the determinant of a 3x3 matrix that has the first vector as the first row, the second vector as the second row, and the unit vectors for the third row. The resulting vector is the cross-product.
The cross-product can be interpreted as the area of the parallelogram formed by the two original vectors, with direction perpendicular to the plane of the parallelogram. This can also be seen as the direction of rotation of a right-hand screw.
The cross-product has many applications in physics, engineering, and computer graphics. It is used to calculate torque, magnetic fields, and angular momentum. It is also used in 3D graphics to calculate lighting and shading effects.
The proof for the properties of the cross-product involves using the properties of determinants and vector operations. It can be shown that the cross-product is distributive, anti-commutative, and follows the right-hand rule. It can also be proved that the magnitude of the cross-product is equal to the area of the parallelogram formed by the two vectors.