Properties of Dot and Cross Product

The dot product of two vectors,is writtenand 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 sinveandare 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 propertywhere %theta is the angle between the vectors starting from the same point.

The cross product is writtenand 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 whereis the acute angle between the two vectors.