1. Sketch the following vector fields
(a) F(x,y) = (2y - x)i + (x + y)j
(b) F(x, y) = \nabla f where f(x, y) = 4x^2 + y^2
Hint for (a): To sketch the vector field F(x, y) = P(x, y)i + Q(x, y)j, find the region in the
(x, y)-plane where P > 0 and Q > 0. In this region F points roughly north-east. Repeat for
the regions where (i) P > 0 and Q < 0, (ii) P < 0 and Q > 0, and (iii) P < 0 and Q < 0.