Assuming we have vector A with elements (A1, A2, A3) and vector B with elements (B1, B2, B3), we can calculate the cross product of these two vectors as:
Cross Product = [(A2*B3) – (A3*B2), (A3*B1) – (A1*B3), (A1*B2) – (A2*B1)]
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 = [(A2*B3) – (A3*B2), (A3*B1) – (A1*B3), (A1*B2) – (A2*B1)]
- 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