The tangent plane at a point Po(f(uovo),g(uo,vo),h (uo,vo)) on a parametrized surfacer(u,v) = f(u,v) i + g(u,v) j + h(u,v) k is the plane through P normal to the vector ru (uovo) xrv (uovo), the cross product ofthe tangent vectors ru (4o,vo) and r(uo.vo) at Po. Find an equation for the plane tangent to the surface at Po. Then find aCartesian equation for the surface and sketch the surface and tangent plane together.VThe circular cylinder r(0,z) = (2 sin (20)) i + (4 sin²e) j+z k at the point Po (√3,3,2) corresponding to (0,z) =(5.2)An equation for the plane tangent to the surface at Po 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.A.B.B.C. Integrate the given function over the given surface.G(x,y,z) = 3z², over the hemisphere x² + y² + z² = 16, z 20The value of the surface integral is.(Type an exact answer, using as needed.)

Answer of the first question is given, plz repost the second question. The equation of a circular…

Answered: The tangent plane at a point Po (f…

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

Find a unit vector normal to the surface x^3- xyz + z^3 = 1 , at the point (1, 1, 1)
Find a vector normal to the surface 3z 3 + x 2 y - y 2 x = 1 at P =(1,-1,1) .
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.
Sketch the space curve represented by the intersection of the surfaces z = x2 + ,y2 x + y = 0 . Then represent the curve by a vectorvalued function using the parameter x = t .
Find the vector equation of the plane tangent to the surface z = x^3 - y^3 at the point (0,1,-1)
Determine the vector equation and the Cartesian equation of the plane tangent to the surface: z = x3 − y3 in the point (0, 1, −1).
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.
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
Find a nonzero vector normal to the plane z−3(x−5)=−4(2−y).
Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and y2+z2=32y2+z2=32 at the point (−4,−4,4)(−4,−4,4).
Find a unit vector n that is normal to the surface 2z^2−x^4−y^4=1 at P=(1,2,3) that points in the direction of the xy-plane (in other words, if you travel in the direction of n, you will eventually cross the xy-plane).
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

Recommended textbooks for you

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS