[I'D APPRECIATE EVEN IF YOU ANSWER ONLY ONE OR TWO OR ANY!!!]Evaluate line integral of (F dot dr) for each of the given vector fields F along the curve C.(a) F = xyzi + yj + zk where C is curve of intersection of the paraboloid z = x^2 + y^2 and the plane z = 1(b) F = xyzi + yj + zk where C is curve of intersection of the paraboloid z = 2 - x^2 - y^2 and the plane z = 1(c) F = 2xyi + xzj + sin(z^2)k where C is boundary of part of the plane 2x + 3y + z = 6 that lies in first octant(d) F(x,y,z) = xyi + 2zj + 3yk ; C is curve of intersection of plane x + z = 1 and cylinder x^2 + y^2 = 9(e) F(x,y,z) = xyi + 2zj + 3yk ; C is boundary of part of plane x + y + z = 1 in first octant(f) F(x,y,z) = (e^z)i + j + x(e^z)k ; C is curve of intersection of the sphere x^2 + y^2 + z^2 = 1 and plane x + y + z = 1.(g) F(x,y,z) = (y + z)i + (x + z)j + (x + y)k ; C is line segment from (1,0,0) to (3,4,2).
[I'D APPRECIATE EVEN IF YOU ANSWER ONLY ONE OR TWO OR ANY!!!]Evaluate line integral of (F dot dr) for each of the given vector fields F along the curve C.(a) F = xyzi + yj + zk where C is curve of intersection of the paraboloid z = x^2 + y^2 and the plane z = 1(b) F = xyzi + yj + zk where C is curve of intersection of the paraboloid z = 2 - x^2 - y^2 and the plane z = 1(c) F = 2xyi + xzj + sin(z^2)k where C is boundary of part of the plane 2x + 3y + z = 6 that lies in first octant(d) F(x,y,z) = xyi + 2zj + 3yk ; C is curve of intersection of plane x + z = 1 and cylinder x^2 + y^2 = 9(e) F(x,y,z) = xyi + 2zj + 3yk ; C is boundary of part of plane x + y + z = 1 in first octant(f) F(x,y,z) = (e^z)i + j + x(e^z)k ; C is curve of intersection of the sphere x^2 + y^2 + z^2 = 1 and plane x + y + z = 1.(g) F(x,y,z) = (y + z)i + (x + z)j + (x + y)k ; C is line segment from (1,0,0) to (3,4,2).
