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)
A vector field is the assignment of a vector to each point in a subset of space in the fields of vector calculus and physics. For instance, a vector field in the plane can be imagined as a group of arrows, each tied to a point in the plane and each with a specific magnitude and direction.
Vector fields are frequently used to simulate many physical phenomena, such as the strength and direction of a force as it varies from point to point or the speed and direction of a fluid traveling across space.
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