method

cross_product

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cross_product(*vs) public

Returns the cross product of this vector with the others.

Vector[1, 0, 0].cross_product Vector[0, 1, 0]   => Vector[0, 0, 1]

It is generalized to other dimensions to return a vector perpendicular to the arguments.

Vector[1, 2].cross_product # => Vector[-2, 1]
Vector[1, 0, 0, 0].cross_product(
   Vector[0, 1, 0, 0],
   Vector[0, 0, 1, 0]
)  #=> Vector[0, 0, 0, 1]

Show source

# File lib/matrix.rb, line 2026
  def cross_product(*vs)
    raise ErrOperationNotDefined, "cross product is not defined on vectors of dimension #{size}" unless size >= 2
    raise ArgumentError, "wrong number of arguments (#{vs.size} for #{size - 2})" unless vs.size == size - 2
    vs.each do |v|
      raise TypeError, "expected Vector, got #{v.class}" unless v.is_a? Vector
      Vector.Raise ErrDimensionMismatch unless v.size == size
    end
    case size
    when 2
      Vector[-@elements[1], @elements[0]]
    when 3
      v = vs[0]
      Vector[ v[2]*@elements[1] - v[1]*@elements[2],
        v[0]*@elements[2] - v[2]*@elements[0],
        v[1]*@elements[0] - v[0]*@elements[1] ]
    else
      rows = self, *vs, Array.new(size) {|i| Vector.basis(size: size, index: i) }
      Matrix.rows(rows).laplace_expansion(row: size - 1)
    end
  end

cross_product

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