'Returns a non-zero point that is orthogonal to the
line containing `self` and the origin.
Examples
>>> from sympy.geometry import Line, Point
>>> a = Point(1, 2, 3)
>>> a.orthogonal_direction
Point3D(-2, 1, 0)
>>> b = _
>>> Line(b, b.origin).is_perpendicular(Line(a, a.origin))
True'

@property
def orthogonal_direction(self):

    dim = self.ambient_dimension
    if (self[0] == S.Zero):
        return Point(([1] + ((dim - 1) * [0])))
    if (self[1] == S.Zero):
        return Point(([0, 1] + ((dim - 2) * [0])))
    return Point(([(- self[1]), self[0]] + ((dim - 2) * [0])))
