Give examples–a formula and an illustration–of two-dimensionalvector fields F?(x,y) with each of the following properties. Youcould do the illustrations by hand.
a) The direction of F? is constant but the magnitude is notconstant.
b) The magnitude |F?| is constant but the direction is notconstant.
c) All the vectors F? along a horizontal line are equal, but F?is not constant overall.
d) F? (x, y) is perpendicular to xˆi + yˆj at every point (x,y).
e) F? is a force field which repels from the origin. It isstrongest near the origin, and weaker farther
away.
