1. Give an example of a vector field F(x, y) in 2-space such that F has constant direction but |F]] is not constant. 2. Give an example of a vector field F(r, y) in 2-space such that || FI| is constant but F is not constant. 3. Write a formula for a vector field in which all vectors are parallel to the r-axis and all vectors on a vertical line have the same magnitude. 4. Write a formula for a vector field in which all vectors point toward the origin and have constant length. 5. Write a formula for a vector field in which all vectors are of unit length and perpendicular to the position vector at that point. 6. Show that the acceleration a of an object flowing in a velocity field F(r, y) = u(x, y) it v(x, y) j is given by a = (uru + ugv) it (Uru + vyv) j. 7. Show that every flow line of the vector field = ri - y j lies on a level curve for the function f(r, y) = ry. 8. Show that every flow line of the vector field & = yi + r j lies on a level curve for the function f(x,y) = x2 - y