The Magnitude of a vector:
Let be a vector then .

The dot product of vectors:

• Let and be two vectors then the dot product of V and U is equal to:
• .

Norm of a vector and the cosine of a central angle:

For a central angle we can rewrite the norm of a vector as relation with the product of the norms of vectors U and V and the product of vectors U and V, namely

The study of vectors and dot products is mentioned in this tutorial. The properties of vectors are discussed in the examples and their use in application problems. The magnitude of a vector in comparison to the vector norm is mentioned in one of the definitions included in one of the example problems.

Dot Products are discussed in this tutorial to assist on the introduction of their application in example problems. The use of a central and its cosine is discussed in one of the definition of a dot product and its norm.

Specific Tutorial Features:
• The properties of vectors and their graphical representation are presented in some examples.
• Definition of a norm and its magnitude is included in one of the example problems.
• Questions are included at the end of the tutorial to test knowledge and some of the concepts discussed in the tutorial.

Series Features:
• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
• Definition slides introduce terms as they are needed.
• Visual representation of concepts
• Animated examples—worked out step by step
• A concise summary is given at the conclusion of the tutorial.

Definition of a vector
              Magnitude of a vector and its properties
              Addition of vectors and examples
              Opposite vectors and examples
              Vector dot product and examples
              Norm of a vector and its relation with the cosine of a central angle