Properties of Dot and Cross Product
The dot product of two vectors,
is written
and is equal to
The dot product of two vectors is a number, and has the following properties:
1. Commutativity
2. Distributity
3. Associativity is meaningless for the dot product sinve
and
are not defined.
4. The dot product of a vector with itself is the square of the magnitude of the vector i.e.
5. The dot product has the property
where %theta is the angle between the vectors starting from the same point.
The cross product is written
and is equal to
The cross product of two vectors is also a vector and has the following properties.
1. Anticommutativity
2. Distributivity
3. Associativity – the cross product is not associative.
but
4. The cross product has the propery
where
is the acute angle between the two vectors.
