vector

is: a mathematical entity which can be represented by a directed line segment (an arrow). [M2.4, M2.5, P2.1]

can be used: to represent a physical quantity that has magnitude and direction. (Such quantities are called vector quantities.) [P2.1]

can be formed: by adding together given vectors (i.e. vector addition) or by multiplying a given vector by a number (i.e. by scaling). [P2.1, P2.2]

usually is denoted: in printed texts by bold symbols such as and

is also denoted: in handwriting by a wavy line underneath it ( etc.); the wavy underline is a printer's mark meaning 'make the character bold'. [M2.4, M2.5]

can be represented: in -dimensions, by scalar components which are usually presented in the form of an ordered multiple such as an ordered pair in two-dimensions or an ordered triple in three-dimensions. [P2.2]