Vector algebra

Vector algebra in grade 12 math:

Introduction to Vector Algebra:

A quantity having both magnitude and direction is called a vector.Examples : displacement, velocity, acceleration, momentum, force, moment of a force, weight etc.Let me tell you what we mean by a vector,the basic meaning of a vector is a vector is a mathematical amount that has both a scale and direction. It is frequently represented by using variable form that is given in bold along with an arrow over it. In physics many quantities defined are vectors. Vector which contains the magnitude of 1 that is denoted using the boldface using a carat (^) is referred as unit vector. A vector of measurement n is an ordered collection of n elements, which are called components.

Once we learn the types of vectors we will be able to make a better judgement about the different types of vectors,

1) Vectors Addition:

Vectors can be the added.

Let A and B be two vectors. We can define a new vector, C = A+B, the “vector addition” of and, by a geometric construction.

• Commutivity.
• Associativity.
• Identity Element for Vector Addition.
• Inverse element for Vector Addition.

2) Scalar Multiplication of Vectors analysis:

Vectors can be the multiplied by real numbers.

Let be a vectors. Let c be real positive number. Then the multiplication of by c is new vector which we denote by the symbol cA. The magnitude of is cA times the magnitude of A.

CA=AC

• Associative Law for Scalar Multiplication.
• Distributive Law for Vector Addition.
• Distributive Law for Scalar Addition.
• Identity Element for Scalar Multiplication.

Lastly let us learn how to express a vector,it will give us a wide picture about the topic

Vectors are represented by directed line segments such that the length of the line segment is the magnitude of the vector and the direction of arrow marked at one end denotes the direction of the vector.

A vector denoted by the [veca] = [vec(AB)] determined by two points A, B such that the magnitude of the algebraic vector is the length of the line segment AB and its direction is that from A to B. The point A is called initial point of the vector [vec(AB)] and B is called the terminal point. Vectors are generally denoted by [veca] , [vecb] , [vecc] … (read as vector a, vector b, vector c, … ).

Hope you like the above example of Vector algebra
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