Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 22

Vectors and Scalars
Various quantities in physics such as temperature, volume and speed can be specified by a real number. Such quantities are called scalars.

Other quantities such as force, velocity and momentum require for their specification a direction as well as a magnitude. Such quantities are called vectors. A vector is represented by an arrow or a directed line segment indicating direction. The magnitude of the vector is determined by the length of the arrow, using an appropriate unit.

Notation for Vectors
A vector is denoted by a bold faced letter such as $\mathbf A$. The magnitude is denoted by $\size {\mathbf A}$. The tail end of the arrow is called the initial point while the head is called the terminal point.

Fundamental Definitions

 * $1.$ Equality of vectors.


 * $2.$ Multiplication of a vector by a scalar.
 * Zero or Null Vector


 * $3.$ Sums of vectors.
 * Parallelogram law for vector addition
 * Difference of vectors


 * $4.$ Unit Vector