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cross product (Definition)

The cross product or vector product is defined by

$\displaystyle \mathbf{A} \times \mathbf{B} = \left ( A_y B_z - A_z B_y \right )... ...\right ) \mathbf{\hat{j}} + \left ( A_x B_y - A_y B_x \right ) \mathbf{\hat{k}}$

Like the dot product, it is useful to look at its geometric definition and properties. Instead of the cosine of the angle between the two vectors the cross product is defined geometrically as

$\displaystyle \mathbf{A} \times \mathbf{B} = \left \vert \mathbf{A} \right \vert \left \vert \mathbf{B} \right \vert \sin \theta \mathbf{\hat{n}} $

It is important to see that the unit vector $\mathbf{\hat{n}}$ is normal to the plane defined by the two vectors with the direction determined by the right hand rule.

It can be easier to remember the definition of the cross product with the determinant formulation

$\displaystyle \mathbf{A} \times \mathbf{B} = \left\vert \begin{matrix} \mathbf{... ...\right ) \mathbf{\hat{j}} + \left ( A_x B_y - A_y B_x \right ) \mathbf{\hat{k}}$



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"cross product" is owned by bloftin.

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Other names:  vector product

Cross-references: determinant, unit vector, vectors, dot product
There are 12 references to this object.

This is version 2 of cross product, born on 2006-07-22, modified 2006-07-28.
Object id is 206, canonical name is CrossProcuct.
Accessed 2296 times total.

Classification:
Physics Classification: 02. (Mathematical methods in physics)
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