# Dot Product

The **Dot product** is the result of **multiplying two vector quantities**. It is often known as a scalar product. This **emphasizes the magnitude of the value only**. The word scaler predicts that the answer will be scaler quantity rather than vector quantity. However, it deals with the single dimension of the value, rather than the three-dimensional value.

**Table of Contents**

## Formula of Dot Product Calculator

The dot product is represented by a dot between two values. i.e

A.B = |A| |B| cos(θ)

**Where,**

|A| = magnitude of the vector quantity A

|B| = magnitude of the vector quantity “B”

θ (theta) = angle between A and B

**Note:**

To gain knowledge about the cross product, click the Cross Product Calculator.

### Properties of Dot Product

The characteristics of dot products are as follow:

**Distributive Quantity**

The value outside the bracket is multiplied by both terms inside i.e.,

A . ( B + c ) = A . B + B . C

**Commutative**

Multiplying the values in either order will have the same result. i.e.,

A . B = B . A

**Bilinear**

The results of combining elements of two vector values in either pattern will be the same. i.e.,

A(RB + C) = R(A . B) + (A . C)

**Scalar Multiplication**

In scalar multiplication, you can take the common values inside the bracket. i.e.,

(C_{1}A) . (C_{2}B) = C_{1}C_{2}(A . B)

### Example

Calculate the dot product of vectors A and B, where A = 8, B = 15, θ = 60°.

**Given data**

A = 8

B = 15

θ = 60°

**To Find**

A.B = ?

**Solution**

As we know,

A.B = |A| |B| cos(θ)

Putting values in the formula:

A.B = (8) (15) cos(60)

A.B = (120) (0.5)

A.B = 60

Therefore, the dot product of vectors A and B is **A.B = 60**

### How to use Dot Product Calculator?

The steps to use the dot product calculator are as follows:

**Step 1: **Enter the values of vector A in the first required input.

**Step 2: **Enter the values of vector B in the second required input.

**Step 3: **The calculator will automatically display an answer on the screen.

### Calculator use

What function does a dot product calculator perform? You just have to put values for the components of each vector and click on the button below. After a few seconds results will appear on your screen. It automatically generates the answer to your problems. You can solve even complex questions using calculatorsbag's calculators. For an advanced-level question, add more than a single value and you will get the solution along with the final answer. You can add negative values, fractions, mixed numbers, and rational numbers to create your question.