Problem 3. Parametrization of surfaces: a) Consider the parametrization 2(15, 3): a: = 3 cos(t) + cos(s) cos(t), y = 3 sin(t) + cos(s) sin(t), z = t | sin(s), for t E [0, 27r] and s E [0, 2a]. The following code in Matlab draws the surface [t,s]=meshgrid(0:pi/10:2*pi+pi/10); x=3*cos(t)+cos(s).*cos(t); y=3*sin(t)+cos(s).*sin(t); z=t+sin(s); surf(x,y,z); axis equal Run this code and attache the surface to your solution. Find the tangent plane on the surface 7T" at t=7r;s=. For a xed 13, the grid line represents the unit circle in space, with the center at the helix :1: = 3 cos(t), y = 3sin(t), 2: = 15. Consider the surface parametrized as 205, 3)::1: = 3 cos(t) + cos(s) cos(t), y = 3 sin(t) + cos(s) sin(t), z = sin(s), for s E [0, 271'] and t E [0, 271']. The surface is called a torus. The following code in Matlab draw this surface: [1: , s] =meshgrid (0 :pi/10 : 2*pi+pi/ 10) ; x=3*cos(t)+cos(s).*cos(t); y=3*sin(t)+cos(s).*sin(t); z=sin(s); surfo,y,z); axis equal Run this code in Matlab, attache the gure to your solution. Find the "exterior" normal vector on the surface at t = s = 0. Find the surface area of the torus. For a xed 13, the grid line represents the unit circle in space, with the center at the circle a; = 3 005(15): y = 3Sin(t) , z = 0