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# How to calculate dot product of two vectors in Python?

• Difficulty Level : Basic
• Last Updated : 25 May, 2021

In mathematics, the dot product or also known as the scalar product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number. Let us given two vectors A and B, and we have to find the dot product of two vectors.

Given that,

and,

Where,

i: the unit vector along the x directions

j: the unit vector along the y directions

k: the unit vector along the z directions

Then the dot product is calculated as:

Example:

Given two vectors A and B as,

## Dot Product of Two Vectors in Python

Python provides a very efficient method to calculate the dot product of two vectors. By using numpy.dot() method which is available in the NumPy module one can do so.

Syntax:

numpy.dot(vector_a, vector_b, out = None)

Parameters:

vector_a: [array_like] if a is complex its complex conjugate is used for the calculation of the dot product.

vector_b: [array_like] if b is complex its complex conjugate is used for the calculation of the dot product.

out: [array, optional] output argument must be C-contiguous, and its dtype must be the dtype that would be returned for dot(a,b).

Return:

Dot Product of vectors a and b. if vector_a and vector_b are 1D, then scalar is returned

Example 1:

## Python

 `# Python Program illustrating``# dot product of two vectors` `# Importing numpy module``import` `numpy as np` `# Taking two scalar values``a ``=` `5``b ``=` `7` `# Calculating dot product using dot()``print``(np.dot(a, b))`

Output:

`35`

Example 2:

## Python

 `# Python Program illustrating``# dot product of two vectors` `# Importing numpy module``import` `numpy as np` `# Taking two 1D array``a ``=` `3` `+` `1j``b ``=` `7` `+` `6j` `# Calculating dot product using dot()``print``(np.dot(a, b))`

Output:

`(15+25j)`

Example 3:

## Python

 `# Python Program illustrating``# dot product of two vectors` `# Importing numpy module``import` `numpy as np` `# Taking two 2D array``# For 2-D arrays it is the matrix product``a ``=` `[[``2``, ``1``], [``0``, ``3``]]``b ``=` `[[``1``, ``1``], [``3``, ``2``]]` `# Calculating dot product using dot()``print``(np.dot(a, b))`

Output:

```[[5 4]
[9 6]]```

Example 4:

## Python

 `# Python Program illustrating``# dot product of two vectors` `# Importing numpy module``import` `numpy as np` `# Taking two 2D array``# For 2-D arrays it is the matrix product``a ``=` `[[``2``, ``1``], [``0``, ``3``]]``b ``=` `[[``1``, ``1``], [``3``, ``2``]]` `# Calculating dot product using dot()``# Note that here I have taken dot(b, a)``# Instead of dot(a, b) and we are going to``# get a different output for the same vector value``print``(np.dot(b, a))`

Output:

```[[2 4]
[6 9]]```

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