Match the following vector fields with the verbal descriptions of the level curves or level surfaces to which they are orthogonal by putting the letter of the verbal description to the left of the number of the vector field.

In all cases it is suggested you sketch the vector field to get a sense of things. In addition, doing so will usually give you the correct insight.

Of course if you prefer random guessing, you should note there are 6! = 720 possible answers :-)

 1. $\mathbf F = -y\mathbf i + x\mathbf j$
 2. $\mathbf F = 2\mathbf i + \mathbf j + \mathbf k$
 3. $\mathbf F = x\mathbf i + y\mathbf j$
 4. $\mathbf F = x\mathbf i + y\mathbf j + z\mathbf k$
 5. $\mathbf F = 2x\mathbf i + y\mathbf j$
 6. $\mathbf F = y\mathbf i + x\mathbf j$

A. ellipses
B. spheres
C. lines
D. circles
E. planes
F. hyperbolas