The tangent plane at a point Po (f(uovo) 9 (uo.vo),h(uo.vo)) on a parametrized surface r(u,v) = f(u, v) i + g(u,v) j+h(u,v) k is the plane through Po normal to the vector ru (uovo) xrv (uovo), the cross product of the tangent vectors ru (40,vo) and rv (uo.vo) at Po. Find an equation for the plane tangent to the surface at Po. Then find a Cartesian equation for the surface and sketch the surface and tangent plane together. The circular cylinder r(0,z) = (3 sin (20))i + (6 sin²0) j+z k at the point Po 3√3 9 2 ¹2 1 -₁)₁ -1 corresponding to (0,z) = - (5-1) An equation for the plane tangent to the surface at Po is (Type an equation using x, y, and z as the variables.)

The tangent plane at a point Po (f(uovo) 9 (uo.vo),h(uo.vo)) on a parametrized surface r(u,v) = f(u, v) i + g(u,v) j+h(u,v) k is the plane through Po normal to the vector ru (uovo) xrv (uovo), the cross product of the tangent vectors ru (40,vo) and rv (uo.vo) at Po. Find an equation for the plane tangent to the surface at Po. Then find a Cartesian equation for the surface and sketch the surface and tangent plane together. The circular cylinder r(0,z) = (3 sin (20))i + (6 sin²0) j+z k at the point Po 3√3 9 2 ¹2 1 -₁)₁ -1 corresponding to (0,z) = - (5-1) An equation for the plane tangent to the surface at Po is (Type an equation using x, y, and z as the variables.)

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.6: Equations Of Lines And Planes

Problem 2E

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