Generalized Vector Cross Product

Given two linearly independent length 3 vectors **a** and **b**, the cross product, \(\mathbf{a} \times \mathbf{b}\) (read "a cross b"), is a vector that is perpendicular to both **a** and **b** thus normal to the plane containing them.

xprod(...)

Arguments

...

N-1 linearly independent vectors of the same length, N.

Value

Returns the generalized vector cross-product, a vector of length N.

Details

A generalization of this idea applies to two or more dimensional vectors.

See: [https://en.wikipedia.org/wiki/Cross_product] for geometric and algebraic properties.

Author

Matthew Lundberg, in a [Stack Overflow post][https://stackoverflow.com/questions/36798301/r-compute-cross-product-of-vectors-physics]

Examples

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

# This works for an 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(1,1,1), c(0,1,0)) # 3d
#> [1] -1  0  1
xprod(c(1,0,0,0), c(0,1,0,0), c(0,0,1,0)) # 4d
#> [1]  0  0  0 -1