# Introduction to Vectors

## A quantity that has both magnitude and direction is called a vector quantity. A quantity that has magnitude only is called a scalar quantity. A line segment that has a particular direction is called a directed line segment. Every directed line segment is associated with length, support and sense. The distance between the initial point and terminal point is called the length (or magnitude) of the vector. The length of a directed line segment is denoted by its modulus. The straight line of an unlimited length of which a directed line segment is a part is called its line of support or simply the support. Two directed line segments having the same or parallel support may have the same or opposite sense. Directed line segments will be considered equivalent, if and only if, they lie on the same or parallel support and have the same length and same sense of direction. The length of the line segment is proportional to the magnitude of the vector. The direction of the line segment is the direction of the vector. The distance between the initial point and terminal point is called the length (or magnitude) of the vector. In mathematics, a quantity which describes a change in position is called a displacement vector. A vector whose initial and terminal points are coincident is called the zero or null vector. Three or more vectors, which neither lie in the same plane nor are parallel to the same plane, are called non-coplanar vectors. Vectors having same or parallel support irrespective of their magnitude and direction are called collinear vectors. Vectors having the same initial point are called co-initial vectors. Vectors having same magnitude and direction, regardless the positions of their initial points are said to be equal. A vector that has the same magnitude as the given vector but the opposite direction is called the negative of the given vector. Two vectors are said to be like vectors if they have the same direction and are said to be unlike vectors if they have the opposite directions. A vector is said to be free or non-localised vector if its origin can be taken anywhere in space. Three or more vectors that lie in the same plane or are parallel to the same plane are called coplanar vectors. Keywords: Notation for a vector, Position vector, proper vectors, localized vectors, reciprocal vectors, non-collinear vectors, unit vectors, non-coplanar unit vectors, free vectors, direction cosines and direction ratios of a vector

To Access the full content, Please Purchase

• Q1

Marks:2

• Q2

Marks:2

• Q3

Marks:2

• Q4

Marks:2