#3: Let F(x, y, z) = (7y, 8x, 7y). Use Stokes' theorem to compute Sc F. dr = where C' is the intersection of the cylinder x² + 1² 36 and the surface : clockwise as viewed from above. 3. The curve C is oriented counter

Q: Consider the surface defined by the following function: x? + y? 2 = Find the points on the given…

A: The equation of the surface is given as, ∅=x2+y2-z The gradient vector at a surface z is given by,…

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (-4, 2, -44).

A: The solution is given as

Q: Use Stokes' Theorem to evaluate of intersection of the plane .x+3y + 5 = 24 with the coordinate…

A:

Q: Let A be an m x n matrix, and let B and C have sizes for which the indicated sums and products are…

A: If the product AB is defined, the entry in row i and column j of AB is the sum of the products of…

Q: Given w f(z,y, 2) = zy²z. Find: Ograd/(1,3,-2) 3. (b) equation of the tangent plane to the surface…

A:

Q: A surface z = f(x, y) is defined implicitly by the equation x +y+ z – e² = 3 – e. - Determine the…

A:

Q: c) Use Stokes' theorem to evaluate F. dr where F = z' i+yJ + xk and C is the triangle with vertices…

A: Stokes theorem is used to find the line integral of the vector point function

Q: Use Stokes's Theorem to evaluate f.7 X F.dŠ, where F (x, y, z) = (y +29)î – xj + x³yk and S is the…

A:

Q: Find VX A for the vector A given by A = -yax + x ay Evaluate Ad A de around the curve x² + y²2 = 1…

A:

Q: Calculate Tu, T, and n(u, v) for the parametrized surface at the given point. Then find the equation…

A: In the given question we have to find the Tu , Tv and n(u, v) and tangent plane.

Q: Evaluate I = f (z, x, y). dr and C is the helix of r(t) = (cost, sin t, 3t) sketch the curve C.

A: Given,               I=∫Cz, x, y·dr, and C is the helix of r(t)=cost, sint, 3t.

Q: Equation of the tangent plane to the surface r(u,v) [5,u,v], 0sus2,0svs2 at the point P: (5,1,1) is…

A:

Q: Let ♬ =. Use Stokes' Theorem to evaluate So F. dr, where C is the curve of intersection of 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: Find an equation of the tangent plane to the surface z = 2a2 + 1y – la – 3y – 1 at the point (5, 3,…

A: Equation of Tangent Plane to the surface F(x, y, z) = 0 at point (x0, y0, z0) is given by ∇F(x0, y0,…

Q: 2. Complete all parts: (a) Find the equation of the curve of intersection of the surfaces y = r² and…

A: Given surfaces: y=x2  and   z=x3 a) Rewriting the above equations in parametric form: Let xt=t…

Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

A:

Q: Sketch the curve associated with the vector function r(t) = . Hint: Show it lies on the surface z?…

A: Given the vector function is r→t=tcost,tsint,t. Skecth the curve associated with the above vector…

Q: Use Stokes' Theorem to evaluate F• dr where C is oriented counterclockwise as viewed from above.…

A: Here use the stokes theorem to find the integral of the function.  And given that the function…

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

A: