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Give examples–a formula and an illustration–of two-dimensional vector fields F?(x,y) with each of the following properties....

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Advance Math

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.

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