Cross product

The cross product is useful for finding a vector which is perpendicular to two vectors. Thus the normal vector of a plane can be found by taking the cross power of two non parrallel vectors in the plane. Another example of the cross product is the vector formulation of angular velocity. The angular velocity of an object about a point is equal to the cross product of the velocity vector and the vector pointing form the point for which the angular velocity is being computed about to the object which the angular velocity is being computed. The angular velocity of an object multiplied by the mass of the object is known as the angular momentum. Combining the phisical laws: conservation of angular momentum and conservation of energy is one way to derive the orbits of the planets.

The magnitude of the vector of the cross product is equal to the product of the magnitude of each vector multiplied by the sign of the angle between them. Geometrically this is the area of the parrallagram formed by each vector. These properties of the cross product can combined to derive the jacobian of an integral. The jacobian of an integral is a quantity used to transform an integral from one coordinate system to another. The cross product and the dot product can be combined to measure volume. The operation is known as the triple product.

Exernal Links

Definition of the cross product from mathworld.