Tangent Planes and Normal Vectors
My Solutions:
Find an equation for the tangent plane and parametric equations for the normal line to the surface z=x^2y at the point (2,1,4).
Script:
```matlab
syms x y z t
Fxy = x^2*y;
a = subs(Fxy, [x,y,z], [2,1,4]);
b = diff(Fxy, x);
b = subs(b, [x,y,z], [2,1,4]);
c = diff(Fxy, y);
c = subs(c, [x,y,z], [2,1,4]);
% Tangent plane equation.
% The form is ax + by + cz = 0 or eqn = 0.
eqn = a*x + b*y + c*z;
% Normal line equations
X = 2 + t*a;
Y = 1 + t*b;
Z = 4 + t*c;
```