The Vector Chapter for Class 11 is one of the most important for Physics when we consider in terms of Board and other competitive exams. This concept is not quite difficult if one aspires to understand the concepts thoroughly. Let us briefly go through the concepts as understood.
In the field of physics Vectors refer to the object which has magnitude that means length and also direction. In general terms they are also called spatial vector and thus it is called Euclidean Vector. When Vectors are added to other vectors and this concept is evident in Algebra. A Vector which is Euclidean is often described by a ray which is a line segment that is directed in a particular direction. In graphical terms there is an arrow that connects from one point to another where one point is the start and one point is the terminal point.
When we talk of a VECTOR we can say it is what is needed to carry from one point to another. The Latin word for Vector is carrier. It was actually first used to denote the planetary revolutions and astronomers tried to ascertain the revolutions around the sun using this theory. The Vector magnitude is the distance from one point to another and thus the direction will mean the displacement and this is from one point to another. We can use the basic arithmetic operations like addition, multiplication and subtraction are used on vectors. These operations obey the basic laws of algebra which are commutative and associative and distributive.
Why do VECTORS play an important part in Physics: This is because any moving body is accelerated and the forces acting on it are all described by vectors. Some of the physical attributes can be vectors. We cannot say that all vectors represent distances or directions except when it is describing itself for displacement or direction. Here the magnitude and direction by given by length and direction as given by an arrow. Apart from Physics if we are to describe it mathematically then it depends on the coordinate system which can describe it.
Thus we know that the vector is the geometric quantity and it has both direction and magnitude. It is a line segment and and this happens in an Euclidean space. In the form of pure mathematics we can say that a vector is the element of a space. Here basically there is no seen or tangible attribute that we can say that this has magnitude and direction. This definition says that the entities are vectors and they are elements of a vector space.
In Physics and Engineering we can say that VECTORS are essential part of the process. They can represent any quantity that has direction and magnitude and they also follow the rules of addition.
When Vector is an arrow then there is a start point and a terminal point. This is a bound vector example. When we consider the magnitude and direction then the initial point is of less importance and then we have is a free vector. If we have two vectors in space then they are known as free vectors if they have same magnitude and direction.
In some magnetic and electric fields we have a system of vectors at some point in the space and that is called a Vector space or Vector field.
Cartesian Space: Here a bound vector will be represented by a coordinates of the start and terminal point. Hence in the Cartesian coordinates we have a free vector and this will be evaluated in terms of the corresponding bound vector and thus the first point will have origin zero. It is then represented by the terminal point of the bound vector.
When we describe a Vector then we can consider couple of things or components or list of numbers also. These are all scalar coefficients and these are set of basic vectors. When the root is transformed by some action in it then the vectors will also change in the corresponding way. The vector will not change but the vector components will change. This is covariant vector.
Covariant vectors are all regular vectors which has distance as the unit such as distance or displacement and distance over some other units such as acceleration. These units have one over distance such as gradient and thus if the units are changed from metre to milimetre for example then there is a scalar vector and there is a displacement of one metre into thousand millimetre and thus there is a contra-variant change accordingly.
Can you solve the question:If the angle between the vectors A and B is theta, the value of the product(BxA)). A is equal to?