The tangent plane at a point Po (f(40.vo) .9 (4o.vo) .h (4o.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) xr, (40,vo), the cross product of the tangent vectors ru (40,vo) and ry (40,v0) 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) = (6sin (20)) i + (12sin´o) j+zk at the point Po (3/3,9,0) corresponding to (0,z) =

The tangent plane at a point Po (f(40.vo) .9 (4o.vo) .h (4o.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) xr, (40,vo), the cross product of the tangent vectors ru (40,vo) and ry (40,v0) 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) = (6sin (20)) i + (12sin´o) j+zk at the point Po (3/3,9,0) corresponding to (0,z) =

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

See similar textbooks

Similar questions

Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
Find a unit vector normal to the surface x^3- xyz + z^3 = 1 , at the point (1, 1, 1)
Consider the surface whose equation is f(x, y) = x^2 - y^2 Determine the vector function r(t) that describes the curve of intersection between f(x,y) and the cylinder of radius 3 that runs along the z axis
Find a vector normal to the surface 3z 3 + x 2 y - y 2 x = 1 at P =(1,-1,1) .
Use Stokes's Theorem to evaluate Integral of the curve from the force vector: F · dr. or the double integral from the surface of the unit vector by the curl of the vector. In this case, C is oriented counterclockwise as viewed from above.F(x, y, z) = z2i + 2xj + y2kS: z = 1 − x2 − y2, z ≥ 0
Let S be the surface obtained by revolving the plane curve 2x=sqrt(9−y2) about the y-axis.Obtain a vector equation for S and use it to find the equation of the tangent plane to S at the point (-1,1,-1).
Find the vector equation of the plane tangent to the surface z = x^3 - y^3 at the point (0,1,-1)
a surface is defined by the parametric form. S(u,v)= X(u,v)i + Y(u,v)j + Z(u,v)k, where 0<= u <=2pi and 0<= v <=1 X(u,v) = (v2+1)cos2u Y(u,v) =vsinu Z(u,v) =-(v2+1) a. determine the normal vector of the surface S b. determine the unit normal vector of S(0,1/2) that point onward
Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and the cylinder of radius 3 wrapped around the y-axis.
Find a vector normal to the surface x2 + yz = 5 at (2, 1, 1).
Find the equations of the normal line and the tangent plane to the parametric surface defined by the vector-valued functionR(u, v) =< v^2−u, u^2−v, 2u+v > at the point (0,2,1).
Find a vector function that parameterizes the curve of intersection between the surfaces y^2-z^2=x-2 and y^2+z=9. Use t as the parameter.