Dot product calculator calculates the dot product of two vectors ** a** and

**in Euclidean space**

*b***Enter**

*.**i, j,*and

*k*for both vectors to get scalar number

*.**a . b*

Vector dot product calculator shows step by step scalar multiplication.

## What is dot product?

Dot product is an algebraic operation that takes two equal-length sequences of numbers usually coordinate vectors, and returns a single number.

Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them.

** a . b **usually read as

**dot**

*a*

*b.*Image credit: “Dot Product” by Math is Fun.

## Dot product formula

Use this equation to calculate dot product of two vectors.

**a × b** = |**a**| |**b**| cos(θ)

Where

|**a**| is length of vector **a**

|**b**| is length of vector **b**

**θ** is the angle between **a** and **b**

We can also find dot product by using the points of both vectors.

*(a _{i }a_{j} a_{k}) . (b_{i} b_{j} b_{k}) = (a_{i} . b_{i} + a_{j} . b_{j} + a_{k} . b_{k})*

Where

** i, j,** and

**refers to**

*k***and**

*x, y,***coordinates on Cartesian plane.**

*z*

References:

Dot Product Formula from tutorial.math.lamar.edu.