text: from sympy import *
  from sympy.physics.vector import *
  from sympy.vector import *
  
  R = CoordSys3D('R')
  t = Symbol('t')
  a = -sin(t)*R.i + cos(t)*R.j + 0*R.k
  b = -cos(t)*R.i + -sin(t)*R.j + 0*R.k
  
  # same
  print(simplify(dot(a, b)))
  print(simplify(a & b))
  
  # same
  print(simplify(a ^ b))
  print(simplify(cross(a, b)))
  
  