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How to Draw Vector Fields?

TopVector field can be defined as representation of a vector on each Point. Association occurs in subset of space which is called Euclidean space. A vector field is usually represented by collection of arrows. These arrows have both magnitude and direction. Speed and direction of a moving fluid throughout space is considered in moving vector field. A vector field can be treated as a vector valued function in Domain of coordinate system.

Vector fields can also be defined on differentiable manifolds. Differentiable manifolds are similar spaces to Euclidean space but they are measured on small scales and may be a complex structure on big scales. A vector field can be defined as a function for both two and three dimensional space. Let’s consider that a two dimensional space has two points (a, b) on it then vector field on this space will be a function R →> that is assigned to each point (a, b) which is a two dimensional vector R→> (a, b).

Vector field is represented in notation as shown below:
R→> (a, b) = M (a, b) i^­ + N (a, b) j^,
Where M, N are called Scalar functions.
Let’s consider following examples to understand how to draw vector fields.
R→> (a, b) = - b i^ + a j^,
Let a = 1 / 2 and b = 1 / 2,
R→> (1 / 2, 1 / 2) = - 1 / 2i^­+ 1 / 2j^,
When a = 3 / 2 and b = 1 / 4 then,
R→> (3/ 2, - 1 / 4) = - 1 / 4i^­ + 3/ 2j^,

In above cases, for point (1 / 2, 1 / 2), we will plot the vector field - 1 / 2i^­ + 1 / 2j^ and similarly for all other points we will plot the vector fields.