The Concept

Vectors constitute one of the several mathematical systems which can be used to handle certain types of problems in geometry, mechanics and other branches of applied mathematics.

A vector is a quantity having both magnitude and direction, such as displacement, velocity, force and acceleration. Any portion of a straight line, where the two end-points are distinguished as initial and terminal, is called a directed line segment. The directed line segment with initial point A and terminal point B is denoted by the symbol or AB. Graphically, a vector is represented by a directed line segment. Analytically, it is represented by a letter with an arrow over it, as in , or in bold type, as in a. A scalar is a quantity having magnitude only but no direction, such as mass, length, time, temperature and any real number. A vector whose initial and terminal points are the same is called a zero vector, 0.

The position vector r of any point P with respect to the origin O is a vector OP. Two vectors and are said to be collinear if they are supported on the same or parallel lines. For such vectors, for some scalar x. A set of vectors is said to be coplanar if they lie on the same plane or the planes in which the different vectors lie are all parallel to the same plane. Three vectors a, b and c are coplanar if for some scalars