A vector is a mathematical object that has magnitude and direction, and satisfies the laws of vector addition. Vectors are used to represent physical quantities that have a magnitude and direction associated with them. For example,
The velocity of an object is a vector. The direction of the vector specifies the direction of travel, and the magnitude specifies the speed.
The force acting on an object is a vector. The direction of the vector specifies the line of action of the force, and the magnitude specifies how large the force is.
Other examples of vectors include position; acceleration; electric field; electric current flow; heat flow; the normal to a surface. Examples of quantities that are not vectors include mass, temperature, electric potential, volume, and energy. These can all be described by their magnitude only (they have no direction) and so are scalars.
A vector is often represented pictorially as an arrow (the arrow’s length is its magnitude, and it points in its direction) and symbolically by an underlined letter , using bold type or by an arrow symbol over a variable . The magnitude of a vector is denoted , or . There are two special cases of vectors: the unit vector has ; and the null vector has .
1.1 Identify whether the following physical quantities should be described as vectors or scalars
(a) Your age
(b) The distance between the Earth and the sun
(c) Forecast wind
(d) The gradient (slope) of a surface
(e) The linear momentum of an object
(f) The speed of light
Go to 2. A First Look At Vector Components