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 °) = 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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