Evaluate F dr, where F(x, y, z)= xyi +4zj +3yk and C is defined by the intersection of the plane x+z = 5 and the cylinder x2 +y² = 9. C is oriented counterclockwise. Apply Stoke's Theorem. Take S to be the ellipse defined by the intersection of the plane and the cylinder. Evaluate over the region D projected down into the xy-plane: D= {(x, y)|x² + y <9}. G(x, y, z)= z-x-5=0 and find VG.

Q: Let e denote the ellipsoid and let L denote the plane 4² = 1 12x + 8y +9z = 51. Using Lagrange…

A:

Q: The surfaces intersect in a space curve C. Determine the projection of C onto the xy-plane.…

A:

Q: Let H be the segment of the hyperbola x-y°= | Connecting (1,0) to (2, J3). Evaluate the line,…

A: Given  H be the segment of hyperbola x2-y2=1 connecting the points (1,0) to (2,3)  we have to…

Q: Find the point of intersection of the line l: x = 2+ 3t, y = 1 – 6t, z = 4 – 2t with the plane - 2x…

A:

Q: Let F(x, y, z) = -3y² + 4z + 6æk and C is the curve of the intersection of the plane x + y + z = 2…

A:

Q: Consider the three-dimensional Euclidean space with coordinates x, y and z. The intersection of the…

A:

Q: Find a vector parametric equation for the ellipse that lies on the plane 4x - 4y + z = -7 and is…

A:

Q: Find an equation for a plane R at a distance 9 from a plane P with equation 2x + 2y - z = 3 .

A:

Q: Evaluate F.ndS for the given F and o. (b) F(x, y, z) = (x² + y) i+ xyj– (2xz + y) k, o: the surface…

A:

Q: Determine the Cartesian form of the plane whose equation in parametric form is: x = 2 + 3s-2t y =…

A:

Q: Find the equation for the sphere centered M(2,-3,2) tangent to the D:6x-3y+2z-11=0 plane

A: we have to find the equation for the sphere centered 2,-3,2 and tangent to the plane 6x-3y+2z-11=0.

Q: Let C be an ellipse in a horizonal plane lying above the xy-plane. Which type of quadric surface is…

A: Given, Let C be an ellipse in a horizontal plane lying above the xy-plane.