The tangent plane at a point Po (f (uo.Vo) 9 (4o.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 (uo.vo) ×rv (uo.vo), the cross product of the tangent vectors ru (uo.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) = (2 sin (20)) i + (4 sin²e) j+z k at the point P₁ (√3,3,2) corresponding to (0,z) = - (²) An equation for the plane tangent to the surface at P is. (Type an equation using x, y, and z as the variables.) A Cartesian equation for the surface is (Type an equation using x, y, and z as the variables.) Choose the correct graph of the surface, point, and tangent plane below. O A. ④ B. y C.

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A: since, y,-x,z3 and, ru,v=u cosv, u sinv,v So, F⇀ru,v=u cosv,-u sinv, v3 Now the normal upward vector…

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A: Here I am attaching image so that you understand each and every step.

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A: This is a problem of vector calculus.

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