Vectors can be multiplied in two different ways: the scalar and vector product. As the name says, a scalar product of two vectors results in a scalar quantity, and a vector product in a vector quantity.

** 1. Scalar Product** (=> applet)

The result of this product is a scalar quantity. The scalar product between two vector is denoted by a thick dot:· = || || cosq _{ab}

Please note: · = · .If is perpendicular to , the scalar product vanishes.

_{ }

** 2. Vector Product **(=> applet)

The result of this product is a vector quantity. The vector product between two vector is denoted by a cross (the product is sometimes also called "cross-product"):x =

Please note: x =-xThe vector is perpendicular to the plane of and , and its magnitude is given by: || = || || sinq

_{AB }The direction of is given by the right hand rule: put the thumb of your right hand along , and the index finger along , then point your middle finger perpendicular to thumb and index finger - this is the direction of .

_{ }If is parallel to , the vector product vanishes.

© W. Bauer, 1999