Calc 3 - Surfaces practice The tangent plane at a point Po (f (u0,vo) g (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 thethe cross product of the tangent vectors r, (uo,vo) and r, (uo,vo) at Po. Find an equation for the plane tangent to the surface at Po.Tu (Uo.vo) ×rvThen find a Cartesian equation for the surface and sketch the surface and tangent plane together.vectorThe circular cylinder r(0,z) = (6sin (20)) i + (12 sin-e) j+zk at the point Po (3/3,9,0) corresponding to (0,z) =

Answered: The tangent plane at a point Po…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Calc 3 - Surfaces practice

The tangent plane at a point Po (f (u0,vo) g (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
the cross product of the tangent vectors r, (uo,vo) and r, (uo,vo) at Po. Find an equation for the plane tangent to the surface at Po.
Tu (Uo.vo) ×rv
Then find a Cartesian equation for the surface and sketch the surface and tangent plane together.
vector
The circular cylinder r(0,z) = (6sin (20)) i + (12 sin-e) j+zk at the point Po (3/3,9,0) corresponding to (0,z) =

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Consider the provided question,

The tangent plane at a point $P_{0} (f (u_{0}, v_{0}), g (u_{0}, v_{0}), h (u_{0}, v_{0}))$

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 $r_{u} (u_{0}, v_{0}) x r_{v} (u_{0}, v_{0})$

The cross product of the tangent vectors $r_{u} (u_{0}, v_{0}) x r_{v} (u_{0}, v_{0}) a t P_{0}$ .

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