Assuming we have vector A with elements (A_{1}, A_{2}, A_{3}) and vector B with elements (B_{1}, B_{2}, B_{3}), we can calculate the cross product of these two vectors as:

**Cross Product** = [(A_{2}*B_{3}) – (A_{3}*B_{2}), (A_{3}*B_{1}) – (A_{1}*B_{3}), (A_{1}*B_{2}) – (A_{2}*B_{1})]

For example, suppose we have the following vectors:

- Vector A: (1, 2, 3)
- Vector B: (4, 5, 6)

We could calculate the cross product of these vectors as:

- Cross Product = [(A
_{2}*B_{3}) – (A_{3}*B_{2}), (A_{3}*B_{1}) – (A_{1}*B_{3}), (A_{1}*B_{2}) – (A_{2}*B_{1})] - Cross Product = [(2*6) – (3*5), (3*4) – (1*6), (1*5) – (2*4)]
- Cross Product = (-3, 6, -3)

You can use one of the following two methods to calculate the cross product of two vectors in R:

**Method 1: Use cross() function from pracma package**

library(pracma) #calculate cross product of vectors A and B cross(A, B)

**Method 2: Define your own function**

#define function to calculate cross product cross <- function(x, y, i=1:3) { create3D <- function(x) head(c(x, rep(0, 3)), 3) x <- create3D(x) y <- create3D(y) j <- function(i) (i-1) %% 3+1 return (x[j(i+1)]*y[j(i+2)] - x[j(i+2)]*y[j(i+1)]) } #calculate cross product cross(A, B)

The following examples show how to use each method in practice.

**Example 1: Use cross() function from pracma package**

The following code shows how to use the **cross()** function from the pracma package to calculate the cross product between two vectors:

library(pracma) #define vectors A <- c(1, 2, 3) B <- c(4, 5, 6) #calculate cross product cross(A, B) [1] -3 6 -3

The cross product turns out to be **(-3, 6, -3)**.

This matches the cross product that we calculated earlier by hand.

**Example 2: Define your own function**

The following code shows how to define your own function to calculate the cross product between two vectors:

#define function to calculate cross product cross <- function(x, y, i=1:3) { create3D <- function(x) head(c(x, rep(0, 3)), 3) x <- create3D(x) y <- create3D(y) j <- function(i) (i-1) %% 3+1 return (x[j(i+1)]*y[j(i+2)] - x[j(i+2)]*y[j(i+1)]) } #define vectors A <- c(1, 2, 3) B <- c(4, 5, 6) #calculate cross product cross(A, B) [1] -3 6 -3

The cross product turns out to be **(-3, 6, -3)**.

This matches the cross product that we calculated in the previous example.

**Additional Resources**

The following tutorials explain how to perform other common tasks in R:

How to Calculate the Dot Product in R

How to Create the Identity Matrix in R

How to Create an Empty Matrix in R