class_docstr: The class used to define vectors.
  
  It along with ReferenceFrame are the building blocks of describing a
  classical mechanics system in PyDy and sympy.physics.vector.
  
  Attributes
  ==========
  
  simp : Boolean
      Let certain methods use trigsimp on their outputs
class_docstr_tok: ["The","class","used","to","define","vectors",".","It","along","with","ReferenceFrame","are","the","building","blocks","of","describing","a","classical","mechanics","system","in","PyDy","and","sympy.physics.vector",".","Attributes","==========","simp",":","Boolean","Let","certain","methods","use","trigsimp","on","their","outputs"]
docstr: The cross product operator for two Vectors.
  
  Returns a Vector, expressed in the same ReferenceFrames as self.
  
  Parameters
  ==========
  
  other : Vector
      The Vector which we are crossing with
  
  Examples
  ========
  
  >>> from sympy import symbols
  >>> from sympy.physics.vector import ReferenceFrame, cross
  >>> q1 = symbols('q1')
  >>> N = ReferenceFrame('N')
  >>> cross(N.x, N.y)
  N.z
  >>> A = ReferenceFrame('A')
  >>> A.orient_axis(N, q1, N.x)
  >>> cross(A.x, N.y)
  N.z
  >>> cross(N.y, A.x)
  - sin(q1)*A.y - cos(q1)*A.z
docstr_tok: ["The","cross","product","operator","for","two","Vectors",".","Returns","a","Vector",",","expressed","in","the","same","ReferenceFrames","as","self",".","Parameters","==========","other",":","Vector","The","Vector","which","we","are","crossing","with","Examples","========",">",">",">","from","sympy","import","symbols",">",">",">","from","sympy.physics.vector","import","ReferenceFrame",",","cross",">",">",">","q1","=","symbols","(","'q1","'",")",">",">",">","N","=","ReferenceFrame","(","'N","'",")",">",">",">","cross","(","N.x",",","N.y",")","N.z",">",">",">","A","=","ReferenceFrame","(","'","A","'",")",">",">",">","A.orient_axis","(","N",",","q1",",","N.x",")",">",">",">","cross","(","A.x",",","N.y",")","N.z",">",">",">","cross","(","N.y",",","A.x",")","-","sin","(","q1",")","*","A.y","-","cos","(","q1",")","*","A.z"]
code: def __xor__(self, other):
      """The cross product operator for two Vectors.
  
      Returns a Vector, expressed in the same ReferenceFrames as self.
  
      Parameters
      ==========
  
      other : Vector
          The Vector which we are crossing with
  
      Examples
      ========
  
      >>> from sympy import symbols
      >>> from sympy.physics.vector import ReferenceFrame, cross
      >>> q1 = symbols('q1')
      >>> N = ReferenceFrame('N')
      >>> cross(N.x, N.y)
      N.z
      >>> A = ReferenceFrame('A')
      >>> A.orient_axis(N, q1, N.x)
      >>> cross(A.x, N.y)
      N.z
      >>> cross(N.y, A.x)
      - sin(q1)*A.y - cos(q1)*A.z
  
      """
  
      from sympy.physics.vector.dyadic import Dyadic
  
      if isinstance(other, Dyadic):
          return NotImplemented
      other = _check_vector(other)
      if other.args == []:
          return Vector(0)
  
      def _det(mat):
          """This is needed as a little method for to find the determinant
          of a list in python; needs to work for a 3x3 list.
          SymPy's Matrix will not take in Vector, so need a custom function.
          You should not be calling this.
  
          """
  
          return (
              mat[0][0]
              * (mat[1][1] * mat[2][2] - mat[1][2] * mat[2][1])
              + mat[0][1]
              * (mat[1][2] * mat[2][0] - mat[1][0] * mat[2][2])
              + mat[0][2]
              * (mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0])
          )
  
      outlist = []
      ar = other.args  # For brevity
      for i, v in enumerate(ar):
          tempx = v[1].x
          tempy = v[1].y
          tempz = v[1].z
          tempm = [
              [tempx, tempy, tempz],
              [self & tempx, self & tempy, self & tempz],
              [
                  Vector([ar[i]]) & tempx,
                  Vector([ar[i]]) & tempy,
                  Vector([ar[i]]) & tempz,
              ],
          ]
          outlist += _det(tempm).args
      return Vector(outlist)
  
imports: from sympy import S, sympify, expand, sqrt, Add, zeros, acos, ImmutableMatrix, simplify
  from sympy.simplify.trigsimp import trigsimp
  from sympy.printing.defaults import Printable
  from sympy.utilities.misc import filldedent
  from sympy.core.evalf import EvalfMixin
  from mpmath.libmp.libmpf import prec_to_dps
label_desc: Use image node_id 17 for calling the Vector obj's underlying member method code with example usage: obj.__xor__(other) and returns: Vector, NotImplemented, Vector, unknown