Draw vector fields

Question

For the following exercises, describe each vector field by drawing some of its vectors.

1.F(x,y)=i+j

2.F(x,y)=3i+xj

Answer 1

1. This field is constant -- at every point the vector points at 45°.

2. To picture this field, draw the function

y = x²/6

If you start at 0 and keep following the arrows of the field,

you will follow this parabola from left to right.

And the field is independent of y.

That means that you can draw all the parabolas of the form

y = x²/6 + C

for all possible constants C.

At any point in the plain the vector F(x,y) is tangent to

the parabola passing through the point (x,y).