Title: Dot Product of Two Vectors

Besides the usual addition of vectors and multiplication of vectors by scalars, there are also two types of multiplication of vectors by other vectors. One type, the dot product, is a scalar product; the result of the dot product of two vectors is a scalar. The other type, called the cross product, is a vector product since it yields another vector rather than a scalar. As with the dot product, the cross product of two vectors contains valuable information about the two vectors themselves.

The dot product of two vectors  and denoted , is

NOTE that the result of the dot product is a scalar.

Example 1:

Vectors v and u are given by their components as follows u = ( -2 , 3, 4) and v = ( 4 , 6, 1.

Find the dot product of the two vectors.

Solution:

Properties of the Dot Product

1. 2. 3. 4.

 Example 2:

Find || v || first using the definition and then using property 3 above where v = (3 , - 4)

Solution :

1. definition:

2. Property 3:

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