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:
· = || || cosqab
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"):
Please note: x = - x
The vector is perpendicular to the plane of and , and its magnitude is given by: || = || || sinqAB
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.