**A dot product**

Multiplication between vectors is a dot product. A dot product is also called a scalar product, because the result of a dot product is always a scalar, that is, a real number.

Let the vectors* a* and* b* be

Then the dot product of the vectors is

In the dot product we multiply the coefficients of the components and adds these products together.

**Example 1**

Calculate the dot product between vectors *a *and* b.*

**Example 2**

Calculate the dot product between vectors *a* and* b.*

The dot product is *0*. This means that the vectors are perpendicular to each other.

For the dot product of *a *and *b*

that is, the dot product of vectors *a* and *b* is the product of the lengths of the vectors multiplied by the cosine of the angle between the vectors.

When the vectors are perpendicular to each other, *cos (90 Â°) = 0*, so

From the definition of the point product in the previous section, a formula is obtained for the angle between the vectors

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