Q:

Write a formula for a two-dimensional vector field which has all vectors parallel to the xx-axis and all vectors on a horizontal line having the same magnitude

Accepted Solution

A:
The formula for a two-dimensional vector field will be:

F = F(x,y) = <u(x,y), v(x,y)> = u i + v j; Where (i,j) are unit vectors in the coordinate directions

To make all vectors parallel to the x-axis
v(x,y)=0
F(x,y) = <u(x,y),0>

To make all vectors on a horizontal line having the same magnitude.
u(x,y) = u(y)
so
F(x,y) = <u(y),0> = u(y) i