# Scalar Product of Vectors

The **scalar product** or **dot product** of two vectors and is equal to:

#### Example

It can also be expressed as:

#### Example

**Magnitude of a Vector**

#### Examples

# Properties of the Scalar Product

### 1Commutative

### 2 Associative

### 3 Distributive

### 4

The dot product of a non-zero vector is always positive

#### Examples

Calculate the scalar product of the following vectors:

1. = (3, 4) and =(-8, 6)

· = 3 · (-8) + 4 · 6 = 0

2. = (5, 6) and =(-1, 4)

· = 5 · (-1) + 6 · 4 = 19

3. = (3, 5) and =(-1, 6)

· = 3 · (-1) + 5 · 6 = 27

If B = { , } is a basis of vectors in the plane, such that | | = || = 2 and cos (, ) = 1/2 and:

= 3 + 2 and = + 2.

Calculate · .

The scalar product is commutative.

cos(, ) = cos (, ) = 1

Subject

Site