Question

Match the following vector fields with the verbal descriptions of the level curves or level surfaces to which they are perpendicular by putting the letter of the verbal description to the left of the number of the vector field.1. F=2i+j2. F = 2i+j+k3. F = 2zi+yj4. F = xi + yj – zk5. Fzi+jk6. F = xi+yj7. F = xi+yj+zk8. F =zij xi yj9. Fi+0.j10. F = yi + xj11. F = 2xi+yj + zk A. planes

B. lines

C. paraboloids

D. spheres

E. circles

F. hyperboloids

G. ellipses

H. ellipsoids

I. hyperbolas

Answer 1

To match the vector fields with the verbal descriptions of the level curves or level surfaces, here is the corresponding match:

1. F=2i+j: E. circles

2. F = 2i+j+k: D. spheres

3. F = 2zi+yj: F. hyperboloids

4. F = xi + yj – zk: B. lines

5. Fzi+jk: A. planes

6. F = xi+yj: G. ellipses

7. F = xi+yj+zk: H. ellipsoids

8. F =zij xi yj: C. paraboloids

9. Fi+0.j: B. lines

10. F = yi + xj: G. ellipses

11. F = 2xi+yj + zk: A. planes

Please note that the matching can vary based on the context and specific definitions given. However, this correspondence should provide a general idea of how the vector fields align with the verbal descriptions of the level curves or surfaces they are perpendicular to.