Let F = (y², x, z²)and S be the part of the paraboloid z = x² + y² with z < 1 and outward facing normal vector. Compute curlF · dŠ using Stokes' Theorem.

Q: 2. (b) Q 3 p sin фа, + p'zag +z cos ф a,

A:

Q: Find a normal vector for the plane with vector equation: [1+3s +2t] 2 x(s, t) = s+t 1+ 3s - t

A: NOTE: Refresh your page if you can't see any equations. . here you can choose any values of s and t…

Q: EXERCISE 4.2 The four corner points of a bilinear surface are Poo = (0, 0, 1), P10 = (1, 0, 0), Po₁…

A: As per the question we are given four distinct points P00 , P01 , P10 , P11 And we have to find :…

Q: Find a point-normal equation for the plane that is represented by the vector equation (x, y, z) =…

A:

Q: find the normal vector of each plane plane 1: 2x-3y+3z=4 plane 2: 2x-y+z=1

A:

Q: Transform each of the following vectors to spherical coordinates at the point specified. a) A = 5a,…

A: Given: The following vectors into cylindrical co-ordinates a) A=5ax at  p4.120°,2b) G=4ax-2ay-4az at…

Q: Verify Stokes' Theorem for the given vector field and surface, oriented with an upward-pointing…

A:

Q: 9. State a vector and scalar equation for the plane passing through Po= (xo, yo, zo) with normal (a,…

A: Given:A plane passing through the point P0=x0, y0, z0. The normal vector to plane is n→ = a,b,c.…

Q: a) Identify and sketch the surface with the given vector equation: r(u,v)=, u between 0 and 2pi, v…

A:

Q: Let L be the line with parametric equations x = 2+t, y = 5-2t, z = 4 + 3t. Let S be the plane that…

A: Given L is the line with parametric equations x = 2 + t , y = 5-2t , z = 4 + 3t . Let S be the plane…

Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: a) Find the unit tangent vector 7(1), unit normal vector Ñ(t), and unit binormal vector B(t) to the…

A:

Q: a. Sketch the surface x2 - y2 + z2 = 4. b. Find a vector normal to the surface at (2, -3, 3). Add…

A:

Q: -y Consider the vector field F = (y²¹, ²²), and the curve defined by 1% + 2 + 2 = 2 and z = c.…

A: Consider the vector field .The curve is given by  and z=c.Substituting, we getThe curve is an…

Q: Compute the unit normal vector field that will give the surface parametrized by r(u, v) = (e"…

A:

Q: Use Stokes' Theorem to evaluate curlF · dS, where

A: Let, F→=xyz , xy , x2yz. Stokes theorem states that ," Where C is the boundary of surface oriented…

Q: Let r(u, v)= [2usin(v), 2ucos(v), 2] be a parametrization of a surface S, where 0sus3,0svs2n. Then…

A: Parametrization of a surface

Q: Three people are standing on a plane (the flat surface kind). The first person is standing at the…

A: Three people are standing on the plane. The first person is at the origin. The second person is at…

Q: Verify Stokes' Theorem for the given vector field and surface, oriented with an upward-pointing…

A: Solving the above question of stokes theorem

Q: Find the flux of F = yi+2xj-3zk through the unit disk centered at (0,3,0) in the plane y=3, oriented…

A: Given F→=yi^+2xj^-3zk^ through the unit disk centered at 0,3,0 in the plane y=3 oriented towards the…