Placing a plane in the correct position with python

Question

I'm trying to place a plane on the surface of a sphere, although I think the math is correct, the resulting figure displays the plane at some point else.

Here is the code to compute and visualize it;

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
plt.style.use('dark_background')

# point and the unit vector
point = np.array([ 349370.39178182, 5570903.05977037, 3085958.36621096])
unit_vector = point/np.linalg.norm(point)

# the math
print(f'plane equation:\nAx + By + Cz + D = 0')
D = np.sum(unit_vector * point)
print(f'D=-(point * unit_vector) = {D:.2f}')
print(f'plane equation:\n{unit_vector[0]:1.4f}x + {unit_vector[1]:1.4f}y + {unit_vector[2]:1.4f}z + {D:.1f} = 0')
print(f'{-1*unit_vector[2]:1.4f}z = {unit_vector[0]:1.4f}x + {unit_vector[1]:1.4f}y + {D:.1f}')
print(f'z = ({unit_vector[0]:1.4f}x + {unit_vector[1]:1.4f}y + {D:.1f}) / {-1*unit_vector[2]:1.4f}')

x = np.linspace(-3e6,+3e6,100)
y = np.linspace(-3e6,+3e6,100)
X,Y = np.meshgrid(x,y)
Z = (0.05477656*X +0.87344241*Y + 6378100.0)/-0.48383662


# plotting stuff
def set_axis_equal_scale(ax, ticks_off=True):
    xl = ax.set_xlim()
    yl = ax.set_ylim()
    zl = ax.set_zlim()
    maxx=max(max(xl), max(yl), max(zl))
    minn=min(min(xl), min(yl), min(zl))
    ax.set_xlim(minn, maxx)
    ax.set_ylim(minn, maxx)
    ax.set_zlim(minn, maxx)
    if ticks_off:
        ax.set_xticks([])
        ax.set_yticks([])
        ax.set_zticks([])

fig = plt.figure(figsize=(5,5))
ax = fig.add_subplot(111, projection='3d')

# plot wireframe
radius = 6.3781e6 # in units m
uu, vv = np.mgrid[0:2*np.pi:200j, 0:np.pi:100j]
xE = radius * np.cos(uu)*np.sin(vv)
yE = radius * np.sin(uu)*np.sin(vv)
zE = radius * np.cos(vv)
ax.plot_wireframe(xE,yE,zE, color='w', alpha=0.1)

ax.scatter(point[0], point[1], point[2], s=500, color='r')
ax.plot([0,point[0]], [0,point[1]], [0,point[2]], color='w', lw=2)

surf = ax.plot_surface(X, Y, Z)
ax.scatter(0,0,0, marker='o', s=900, color='b')

ax.view_init(25, -190)
ax.axis('off')
set_axis_equal_scale(ax)

I expect the plane to be on where the red marker is and perpendicular to the white line connecting the center and the red marker.

[here is the image][1] [1]: https://i.stack.imgur.com/LHPzW.png