# Dot Product of Vectors in R Programming

• Last Updated : 25 Aug, 2020

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,

A = 3i + 5j + 4k,

and

B = 2i + 7j + 5k

Dot Product = 3 * 2 + 5 * 7 + 4 * 5 = 6 + 35 + 20 + 61

#### Computing Dot Product in R

R language provides a very efficient method to calculate the dot product of two vectors. By using dot() method which is available in the geometry library one can do so.

Syntax: dot(x, y, d = NULL)

Parameters:

x: Matrix of vectors

y: Matrix of vectors

d: Dimension along which to calculate the dot product

Return: Vector with length of dth dimension

Example 1:

## R

 `# R Program illustrating``# dot product of two vectors`` ` `# Import the required library``library``(geometry)`` ` `# Taking two scalar values``a = 5``b = 7`` ` `# Calculating dot product using dot()``print``(``dot``(a, b, d = ``TRUE``))`

Output:

``` 35
```

Example 2:

## R

 `# R Program illustrating``# dot product of two vectors`` ` `# Import the required library``library``(geometry)`` ` `# Taking two complex values``a = 3 + 1i``b = 7 + 6i`` ` `# Calculating dot product using dot()``print``(``dot``(a, b, d = ``TRUE``))`

Output:

``` 15+25i
```

Example 3:

## R

 `# R Program illustrating``# dot product of two vectors`` ` `# Import the required library``library``(geometry)`` ` `# Taking two simple vectors``a = ``c``(1, 4)``b = ``c``(7, 4)`` ` `# Calculating dot product using dot()``print``(``dot``(a, b, d = ``TRUE``))`

Output:

``` 23
```

Example 4:

In this following example let’s take two 2D arrays and calculate the dot product of these two. To create a 2D array in R please refer Multidimensional Array in R.

## R

 `# R Program illustrating``# dot product of two vectors`` ` `# Import the required library``library``(geometry)`` ` `# Taking two 2D array``vector1 = ``c``(2, 1)``vector2 = ``c``(0, 3)``a = ``array``(``c``(vector1, vector2), dim = ``c``(2, 2))``vector1 = ``c``(4, 2)``vector2 = ``c``(9, 3)``b = ``array``(``c``(vector1, vector2), dim = ``c``(2, 2))`` ` `# Calculating dot product using dot()``print``(``dot``(a, b, d = ``TRUE``))`

Output:

``` 10  9
```

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