222 - Topic 08 - Tangent planes and normal lines

var('x,y,z') # Write the equation as F(x,y,z) = 0 @interact def _(F = input_box(default=y*ln(x*z^2)-2,label='0 = F(x,y,z) = '),location=input_grid(1, 3, default=[e,2,1], label = "Location (x,y,z) = ", width=3)): x0 = location[0][0] y0 = location[0][1] z0 = location[0][2] Fx = diff(F,x) Fy = diff(F,y) Fz = diff(F,z) a = Fx(x=x0,y=y0,z=z0) b = Fy(x=x0,y=y0,z=z0) c = Fz(x=x0,y=y0,z=z0) G = implicit_plot3d(F,(x,x0-1,x0+1),(y,y0-1,y0+1),(z,z0-1,z0+1)) G += point3d((x0,y0,z0),color='red',size=25) G += arrow((x0,y0,z0),(x0+a,y0+b,z0+c),color='green') G += implicit_plot3d(a*(x-x0)+b*(y-y0)+c*(z-z0),(x,x0-1/2,x0+1/2),(y,y0-1/2,y0+1/2),(z,z0-1,z0+1),color='yellow') show(G,aspect_ratio=true)