In the pane on the right, drag the blue dot within the [math]uv[/math]-square to see how a surface is parametrized with the variables [math]u[/math] and [math]v[/math]. [br] [math]\mathbf{r}\left(u,v\right)=\left\langle f\left(u,v\right), g\left(u,v\right), h\left(u,v\right)\right\rangle[/math][br]You can also change the bounds on [math]u[/math] and [math]v[/math], and you can change the functions [math]f[/math], [math]g[/math], and [math]h[/math].[br][br]The plane tangent the surface at the point [math]P_0[/math] (corresponding to [math]\left(u_0,v_0\right)[/math]) is perpendicular to the cross product [math]r_u(u, v) \times r_v(u, v)[/math] evaluated at the point [math]\left(u_0,v_0\right)[/math].

[i]This applet was developed for use with [url=https://www.pearson.com/en-us/subject-catalog/p/interactive-calculus-early-transcendentals-single-variable/P200000009666]Interactive Calculus[/url], published by Pearson.[/i][br]