# Dot Product Calculator

Dot Product is the **product** of the Euclidean magnitudes of the two vectors and the cosine of the angle between them.

## What is Dot Product Calculator?

'Cuemath's Dot Product Calculator' is an online tool that helps to calculate the dot product of the given two vectors. Cuemath's online Dot Product Calculator helps you to calculate the dot product in a few seconds.

## How to Use Dot Product Calculator?

Please follow the below steps to calculate the dot product:

**Step 1:**Enter the coefficients of two vectors in the given input boxes.**Step 2:**Click on the**"Calculate"**button to calculate the dot product.**Step 3:**Click on the**"Reset"**button to clear the fields and enter the different values.

## How to Find Dot Product Calculator?

**Vectors** are quantities with both magnitude and direction. Vectors help to simultaneously represent different quantities in the same expression.

The standard form of representation of a vector is:

**a = a _{1}i^ + a_{2}j^ + a_{3}k^**

**b = b _{1}i^ + b_{2}j^ + b_{3}k^**

Where a_{1}, b_{1}, c_{1,} and a2, b_{2}, c_{2}are numeric values, and i^, j^, k^ are the unit vectors along the x-axis, y-axis, and z-axis respectively.

The dot product is also known as the scalar product. It’s called a scalar product because this multiplication gives magnitude as a result. It's a way of representing the multiplication between two (or more) vectors. The dot product is a multiplication of the two vectors. The dot product is represented by a.b

** Dot product(a.b) = (a _{1} × b_{1}) + (a_{2} × b_{2}) + (a_{3} × b_{3})**

**Solved Example:**

Find the dot product of two vectors a = 4i + 2j – 5k and b = 3i – 2j + k?

**Solution:**

Given a = 4i + 2j – 5k and b = 3i – 2j + k

a.b = (a_{1} × b_{1}) + (a_{2} × b_{2}) + (a_{3} × b_{3})

a.b = (4 × 3) + (2 × (-2)) + ((-5) × 1)

= 12 - 4 - 5

= 3

Therefore, the dot product of two vectors is 3.

Similarly, you can use the calculator to find the dot product of two vectors for the following:

- a = 4i + 2j - 5k and b = -1i + 4j - 3k
- a = -2i - 5k and b = -7i + j + k