by Elsie esq.
A vector is defined as a specific mathematical structure that is utilized in mathematics and in geometric applications it is especially defined as a quantity with the magnitude and path .Vectors have the potential to find the directions of defined object with their magnitude. As an instance wind is defined in terms of each speed as effectively as path or if take an example of moving object then it also defined or express in forces applies on that body and the direction of the applied force .On a Cartesian coordinate plane positions of the object or locations of points are expressed in terms of ordered pair ( x , y ) that is a particular instance of vector .For a vector ( x , y ) is defined as a certain distance that is a magnitude from and an angle that is defined the path connected to the origin ( , ).For simplifying the issues associated to the three – dimensional geometry vectors are quite useful .
In basic terms scalar are referred to as as real numbers and vectors are named as of dimension n that is an ordered collection of elements n , that are named as components . Scalar quantities usually represent as the variables just as we define them in algebra but when we talk about the vector quantities than they are represented in type of bold and capital letters like X. A vector can also be represented with a right – handed arrow. If an n – dimensional vector X has n components then it is denoted symbolically as:
X = X1 , X2 , . . . . , Xn > or X = ( X1 , X2 , . . . . , Xn )
The above representation is understood in terms of numerical values as ( 2 , -five ) , ( -1 , , 2 ) and
( PI , a , b , two / 3 ) , these are the examples of vectors that have the dimensions 2 , 3 , four respectively . If two corresponding elements are equal then their vectors are also referred to as as the equal vectors.
When we speaking about the Vector Calculator it is really useful on-line tool for the students .by this tool students get the answers of their values without delay .In vector there are several operations like addition , subtraction , multiplication etc that are also supported by the Vector calculator like Vector addition calculator or cross item calculator and so forth. In the vector calculatoruser can enter the real number as nicely as the complicated quantity for carrying the calculations. Let’s take an example of calculation by the vector calculator for a subspace E of X4 that is generated by two of the vectors
V1 = ( 1 , two , 3 , four ) and V2 = ( 1 , -1 , -1 , 1 ) and V1 , V2 are the orthogonal elements correspond to the linear system then define the E . There are one more two vectors v1 = ( -5 , -2 , three , ) and v2 = ( -2 , -five , , three ) .
Then by the linear method, E is defined as:
-5 x1 – 2 x2 + three x3 = ,
-2 x1 – 5 x2 + 3 x3 =