Let S be the parametric surface: r(u, v) = (u2, u cos v, u sin v). Find the tangent plane equation of S at (1, 1, 0).
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- 2. Find an equation of the tangent plane to the parametric surface F(u, v) = (, 2uv, uv?) at the point (-2, -4, –4).Sketch the parametric curve of r(t) =< 2cost,2sin t,3 >.Then, find and draw thetangent vector r'(0).Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces z = x2 + y2 , z = 4 − y at the given point (2, −1, 5).
- Find an equation of the tangent plane to the parametric surface R(u, v) = ((u - sin u) cos v, (1 - cos u) sin v, u) at the point where u = v= TT IN 2The two surfaces x2 + y2 + z2 = 6 and 2x2 + 3y2 + z2 = 9 intersect at the point(1,1,2). Find the angle between the tangent planes at the point(1,1,2). Also, find the tangent vector to the curve in which surface intersect?Consider the surface S parametrized by R(u, v) = (uv, sin u, cos v). Find an equation for the tangent plane to S at the point (, 1, ).
- Find an equation of the tangent plane to the following parametric surface,r(u, v) = (u2 + 6) i + (v3 + 8u) j + (u + 3v) k ,at the point (7, 7, −2).Write the equation in the form ax + by + cz + d = 0, where a, b, c, and d have no common factors. Then enter the values of a, b, c, and d (in that order) into the answer box below, separated with commas.Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces x2 + y2 + z2 = 14, x − y − z = 0, at the given point (3, 1, 2).Write the parametric equation of the bilinear surface corresponding to four points P(0 0)= 0.25 0 P(1 0)- 0.75 0 P(0.1)- 0.75 0.9 PEL.A F 0.25.0.8 .Also calculate the tangent and normal vectors at the mid-point of the surface.
- Let C be the curve of intersection of the two surfaces x³ + 2xy + yz = 7 and 3x²-yz = 1. Find parametric equations of the tangent line to C at (1,2,1).Find an equation of the tangent plane to the parametric surface R(u, v) = ((u - sin u) cos v, (1 - cos u) sin v, u) ㅠ NIE at the point where u = v= 2Equation of the tangent plane to the surface 7 (u,v) at (uo,Vo) is given by 7-7(uo, Vo)× Ñ(uo,Vo)=0. Select one: O True O False