rcross-product# R - Compute Cross Product of Vectors (Physics)

What am I doing wrong?

```
> crossprod(1:3,4:6)
[,1]
[1,] 32
```

According to this website:http://onlinemschool.com/math/assistance/vector/multiply1/

It should give:

```
{-3; 6; -3}
```

See also What is R's crossproduct function?

Solution

Here is a generalized cross product:

```
xprod <- function(...) {
args <- list(...)
# Check for valid arguments
if (length(args) == 0) {
stop("No data supplied")
}
len <- unique(sapply(args, FUN=length))
if (length(len) > 1) {
stop("All vectors must be the same length")
}
if (len != length(args) + 1) {
stop("Must supply N-1 vectors of length N")
}
# Compute generalized cross product by taking the determinant of sub-matricies
m <- do.call(rbind, args)
sapply(seq(len),
FUN=function(i) {
det(m[,-i,drop=FALSE]) * (-1)^(i+1)
})
}
```

For your example:

```
> xprod(1:3, 4:6)
[1] -3 6 -3
```

This works for any dimension:

```
> xprod(c(0,1)) # 2d
[1] 1 0
> xprod(c(1,0,0), c(0,1,0)) # 3d
[1] 0 0 1
> xprod(c(1,0,0,0), c(0,1,0,0), c(0,0,1,0)) # 4d
[1] 0 0 0 -1
```

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