intersection of plane and surface

I have 3 points that forms a plane and a sphere with radius 6378.137 that is earth. I want the intersection of plane and sphere.

below is my code , it is not showing sphere and plane intersection

clc;
clear all;
pos1 = [1721.983459                 6743.093409                  -99.586968 ];
pos2 = [1631.384326                   6813.006958                     37.698529];
pos3 = [1776.584150                   6686.909340                     60.228160];
normal = cross(pos1-pos2, pos1-pos3)
syms x y z
p = [x y z];
planefun = dot(normal,p-pos1);
zplane = solve(planefun,z)
figure
ezmesh(zplane)
hold on
[x, y, z] = sphere;
r = 6378.137;
x = x*r;
y = y*r;
z = z*r;
surf(x,y,z)

Answer 1

[Star Strider]

Use fsurf (or fmesh) and then use the view function to rotate it for best results —

pos1 = [1721.983459                   6743.093409                    -99.586968];
pos2 = [1631.384326                   6813.006958                     37.698529];
pos3 = [1776.584150                   6686.909340                     60.228160];
normal = cross(pos1-pos2, pos1-pos3)

normal = 1×3

1.0e+04 * 1.8887 2.1975 0.1273

syms x y z
p = [x y z];
planefun = dot(normal,p-pos1);
zplane = solve(planefun,z)

zplane = 

figure
fsurf(zplane, 'r')
hold on
[x, y, z] = sphere;
r = 6378.137;
x = x*r;
y = y*r;
z = z*r;
surf(x,y,z)
view(60,30)
axis([-10000  10000    -10000  10000    -10000  10000])

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