# How to Calculate the Dot Product in R (With Examples)

Given vector a = [a1, a2, a3] and vector b = [b1, b2, b3], the dot product of vector a and vector b, denoted as a · b, is given by:

a · b = a1 * b1 + a2 * b2 + a3 * b3

For example, if a = [2, 5, 6] and b = [4, 3, 2], then the dot product of a and b would be equal to:

a · b = 2*4 + 5*3 + 6*2

a · b = 8 + 15 + 12

a · b = 35

In essence, the dot product is the sum of the products of the corresponding entries in two vectors.

## How to Calculate the Dot Product in R

There are two ways to quickly calculate the dot product of two vectors in R:

Method 1: Use %*%

The following code shows how to use the %*% function to calculate the dot product between two vectors in R:

```#define vectors
a <- c(2, 5, 6)
b <- c(4, 3, 2)

#calculate dot product between vectors
a %*% b

[,1]
[1,]   35```

The dot product turns out to be 35.

Note that this function works for data frame columns as well:

```#define data
df <- data.frame(a=c(2, 5, 6),
b=c(4, 3, 2))

#calculate dot product between columns 'a' and 'b' of data frame
df\$a %*% df\$b

[,1]
[1,]   35```

Method 2: Use the dot() function

We can also calculate the dot product between two vectors by using the dot() function from the pracma library:

```library(pracma)

#define vectors
a <- c(2, 5, 6)
b <- c(4, 3, 2)

#calculate dot product between vectors
dot(a, b)

[1] 35```

Once again, the dot product between the two vectors turns out to be 35.

The following tutorials explain how to calculate a dot product using other statistical software:

May 13, 2024
April 25, 2024
April 19, 2024
April 18, 2024

## One Reply to “How to Calculate the Dot Product in R (With Examples)”

1. Jul says:

Beware that the `a %*% b` gives a matrix, not a vector (of length one)

One can also use `sum(a * b) `