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"):x
=
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.
© W. Bauer, 1999