# Dot Product of Vectors in R Programming

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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