Vector Nnalysis

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Analysis of vector field is the important topic from vector chapters in mathematics. Vector field is containing with the related topics like curl, gradient, divergence, and so on. In this order, line integrals are the important one of the vector filed analysis.

Vector field analysis is mainly deals with its dimensions. Vector fields have two types of dimensions. Here we are going to explain about those details in vector field analysis.

Explanations of vector field analysis:

Generally vector fields are things, which are we have solved and determined in previous topics of vectors, in the form of gradient vector fields.

This is considered to let us work with more general fields and, in the previous vector fields, with line integrals, a topic that builds on the notion of a vector fields.

Types of vector fields:

Here, there are two important vector fields are given below:

Two dimensional vector fields, and
Three dimensional vector fields.

We have to explain both vector fields by below.

Explanations for two vector fields:

Vector fields in two dimensions:

Definition:

A ...
... two dimension vector field is defined by a function which connections with each vector of each point in the field of the function. (Domain = field).

In this two dimensions a vector field V can be denoted by the appearance

`V (x, y) = (p(x, y), q(x, y))`

Two dimension vector field analysis – picture representation:

analysis of vector field

The functions `p ` and `q ` may be randomly defined, or they may depend on some other function, as in the case of a gradient vector field.
This demonstration displays a vector field, allows us to define the field and its domain.
It shows a vector field in two dimensions with the vectors denoted (represented) by arrows.
The functions `p(x, y)` & `q(x, y)` are, define the vector field of ,

` V (x, y) = (p(x, y), q(x, y)).`

Vector fields in three dimensions:

Definitions:

In this three dimensions a vector field ‘`V` ’ can be denoted as the appearance of

` V (x, y, z) = (p(x, y, z), q(x, y, z), r(x, y, z)).`

Three dimension vector field analysis – picture representation:

analysis of vector fields

The functions `p, q` , and `r` may be randomly defined, or they may depend on some other function, as in the case of a gradient vector field.
This expression displays a vector field in three-space, allows us to define the field and its domain.
The vector field is defined over a rectangular field and has the form, (domain = field).

`V (x, y, z) = (p(x, y, z), q(x, y, z), r(x, y, z)).`

These all above analysis & explanations and examples make clears about the vector filed analysis.

When we are at right to select the source of the vector at any point, then it is called as a free vector. A quantity contain both scale and direction is called as vector. If some items or entity or objects are arranged in based on some rule this is called as pattern. Let us see free vector pattern in this article.

Free Vector Pattern:

Definition of pattern:

If some items or entity or objects are arranged in based on some rule this is called as pattern.

Exampl for pattern:

1`veca` , 6`veca`, 11`veca`, 16`veca`, 21`veca`, 26`veca` …

In the above pattern rule is start at 1`veca` and add 6`veca` each time.

Definition of vector:

A quantity contain both scale and direction is called as vector.

Check this scalar fields awesome i recently used to see.

Representation of vector:

Vector is represented by directed line segment. Straight line segment means the duration of line segment is the magnitude of the vector and the way of arrow blotted at one end denotes the direction of the vector.

Vector is represented by `veca`.

Operation of vectors:

Addition of vector
Subtraction of vector
Multiplication of vector

Types for vectors:

Zero or null vector
Unit vector
Co – initial vector
Co – terminus vector
Collinear or parallel vector
Co – planer vector
Negative vector
Free and localized vector

Free vector:

When we are at right to select the source of the vector at any point, then it is called as a free vector.

Example for Free Vector Pattern:

Free vector is used to state the selection of source of the vector at any point.

Example 1:

2`veca` , 4`veca`, 6`veca`, 8`veca`, 10`veca`, …

The above is present in the free vector pattern structure. The rule is start from 2 and add 2 in each step and we select the source of the vector so 2`veca` , 4`veca`, 6`veca`, 8`veca`, 10`veca`, … is a free vector pattern.

Example 2:

1`veca`, 6`veca`, 18`veca`, 24`veca`, 30`veca`, …

The above is present in the free vector pattern structure. The rule is start from 1 and multiply 6 in each step and we select the source of the vector so 1`veca`, 6`veca`, 18`veca`, 24`veca`, 30`veca`, … is a free vector pattern.

Learn more on about Online Length Conversion and its Examples. Between, if you have problem on these topics Plotting Graph, Please share your comments.