Cross Product of 3D Vectors or Matrices

Computes the cross product in three-dimensional space for vectors or matrices. For matrices, the operation can be applied row-wise or column-wise.

Usage

crossProd(x, y, orientation = c("rows", "cols"))

Arguments

x: a numeric or complex vector of length 3, or a matrix with one dimension of length 3.
y: a numeric or complex vector or matrix with the same dimensions as x.
orientation: character string specifying whether vectors are stored in rows or columns when matrices are supplied. Must be one of "rows" or "cols". Ignored if x and y are vectors.

Value

a vector of length 3 if inputs are vectors.
a matrix if matrices are supplied. Dimension names along the vector axis are propagated from x, the component axis is labelled x, y, z.

Details

For vectors $x = (x_1, x_2, x_3)$ and $y = (y_1, y_2, y_3)$, the cross product is: $$ x \times y = (x_2 y_3 - x_3 y_2,\; x_3 y_1 - x_1 y_3,\; x_1 y_2 - x_2 y_1) $$

For matrix inputs:

orientation = "rows": each row is treated as a vector (requires ncol(x) == 3)
orientation = "cols": each column is treated as a vector (requires nrow(x) == 3)

Numeric and complex inputs can be mixed; standard R coercion rules apply.

Examples

# Vector case
crossProd(c(1,0,0), c(0,1,0))
#> [1] 0 0 1

# Row-wise
x <- matrix(c(1,0,0,
              0,1,0), ncol = 3, byrow = TRUE)
y <- matrix(c(0,1,0,
              0,0,1), ncol = 3, byrow = TRUE)
crossProd(x, y, "rows")
#>      x y z
#> [1,] 0 0 1
#> [2,] 1 0 0

# Column-wise
x <- matrix(1:9, nrow = 3)
y <- matrix(9:1, nrow = 3)
crossProd(x, y, "cols")
#>   [,1] [,2] [,3]
#> x  -10  -10  -10
#> y   20   20   20
#> z  -10  -10  -10