Basic Concepts of Vectors (FSC part 1)

Basic Concepts of Vectors:
1. Vectors:
    As we study that some physical quantities which have requires both magnitude and and Direction for their complete description, like as velocity, acceleration and force. They are vectors. usually in writing use bold text for describe the vectors, Let point A, B and C is Vectors we write A, B and C.
    A vectors is represented graphically by by a directed line segments with an arrow head.


2. Rectangular Coordinate System:
    Two reference lines drawn at night angles to each other. Coordinate axes and their point of intersection is known as origin. This system of coordinate axes is called Cartesian of rectangular coordinate system.

3. Addition of Vectors:
    Given two vectors A and B, their sums obtained by drawing their representative lines in such a way that tail of vector B coincides with the head of B. The vector sum is also called resultant and is indicate by R. Thus R = A + B. Similarly the sum
A + B is illustrated by back lines. Therefore, we can say that
    A + B = B + A

4. Resultant Vectors:
    The resultant of a number of vectors of the same kind-force vectors for example, is that signal vector which would have the same effect as all the original vectors taken together.

5. Vector Subtraction:
    The subtraction of a vector is equivalent to the addition of the same vector with its direction reserved. Thus, two subtract vector B from vector A, reverse the direction of B and A it to A.

    A - B = A + (-B)

6. Unit Vector:
    The product of a vector in a given direction is vector with magnitude on in that direction. It is used to represents the direction of a vector.
    A unit in the direction of A is written as A^ , which we read as ' A hat' , thus
        A = A A^ ( A hat)

7. Null Vector:
    Null vector is a vector of zero magnitude and any direction. For example, the sum of a vector and its negative vector is a null vector.

8. Equal Vector:
    Vector A and B are called equal vector if the both vector have same direction and magnitude. This mean that parallel vectors of the same magnitude are equal to each other.

9. Rectangular components of a vector:
    A components of a vector is its effective value in a given direction. It considered as the resultant of the vector components along the specific directions.
    Let there be a vector A represented by OP making angel with the x-axis. The projection OM of vector OP on x-axis and projection ON of vector OP on y-axis. OM being along x-direction is represented by Ax i^d ON = MP along y-direction is represented by Ay ^. By the rule of head to tail.
    A = Ax ^ + Ay j^
triangle MOP, the magnitude of  Ax i^ or x-components A is,
    Ax = A sin (theta)
    Ay = A cos (theta)

9. Position Vector:
    The position vector r is a vector that describes the location of a point with respect to origin, it is represented by r^.
Hence,
    r = a i^ + b j^