4. Let S is the surface z = 5- - y, 1s z in R. Let S be oriented with the normal vector pointing upward direction. (a) Let F(r, y, 2) = (y, z, 3). Use Stokes Theorem to evaluate Lv x F) - dš (b) Verify Stokes' theorem for part (a).

Q: Find the equation of the tangent plane at point (2,3,0) for the parametric surface given by (u,v) =…

A:

Q: 2 = 8 at the

A:

Q: A particle moves along line segments from the origin to the points (2, 0, 0), (2, 3, 1), (0, 3, 1),…

A: Given that a particle moves along line segments from the origin to the points (2, 0, 0), (2, 3, 1),…

Q: Consider the function f(x, y) = (e - 3x) cos(y). Suppose S is the surface z = f(x, y). (a) Find a…

A:

Q: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

A:

Q: x² + y³. 2 = Consider the surface S of equation (1, 1, v), An equation for the tangent line tangent…

A: We have to find the equation of tangent line.

Q: Let F(x, y, z) = xye" – 2° Ja and P(1,0, –1). Let S be the surface defined by the equation xye" –…

A:

Q: Let F = (y², x, z²)and S be the part of the paraboloid z = x² + y² with z < 1 and outward facing…

A:

Q: Find the surface area of the helicoid (spiral ramp) with vector equation F(u, v) = (u cos v, u sin…

A: The surface area of the helicoid can be computed using the surface integral formula:   ∫∫Rru×rvdA…

Q: Find symmetric equations of the normal to the surface, r (u, v) = at a point (1, 1, 3

A: given ru,v=&lt;u2,v2,u+2v&gt; therefore ru=∂∂uu2i+∂∂uv2j+∂∂uu+2vk=2ui+0j+k…

Q: Consider surface S of the cone S : z = 2/a2+ y² at the point P(1, , V5). (a) Determine the vector…

A:

Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

A:

Q: 6. Use the Normal Vector to a Smooth Parametric Surface to find the equation of the tangent plane to…

A:

Q: State and illustrate Stokes' Theorem using the surface of the cone z= √√²+y³ and below the plan z =…

A:

Q: Consider the surface S of equation 2 = x² + y*" An equation for the tangent line tangent to S at…

A:

Q: Evaluate the line integral by stokes theorem where F(vector)=[ 0, xyz ,0] , C is the boundary of a…

A: Calculate curl:  curlF=ijk∂∂x∂∂y∂∂z0xyz0         =i-xy+kyz

Q: -a-) Find the surface normal vector the sphere with radius √TT centered at (0,1,0) ie x² +(y-1)² +…

A: Since you have posted and asked multiple questions, we will solve the first question for you. If you…

Q: Calculate % F-dr where

A: Given,           F=xyi+2zj-xykand C is the intersection of the of the plane y=z+2 withcylinder…

Q: y Consider the surface of equation z = What is the equation for the tangent line to S at x2+y4 * the…

A: Solution

Q: The unit normal vector to the surface x'y + 2xz? = 8 at the point %3D (1,0, 2) is

A: