I am stuck in meaning of vectors I am reading Calculus by Apostol in which vectors are defined as n-tuple of numbers upto a triple of numbers it looked significant as it represented a direction and magnitude in space but why quadruple and other higher elements are considered vectors is still out of my thinking...
Please help me with this..
On
A line segment (with "magnitude and direction") between two points of space is often called an "geometric vector". The two points may, respectively,be regarded as the argument and image of a TRANSLATION. It is the translation, (a function), which is the vector.... it satisfies the axioms of a vector space. 2-3- n-Space may be turned into vector spaces by addition and external multiplication. Translations on those sets may also be turned into (isomorphic) vector spaces by composition and external multiplication.
In general two points, a and f(a), in the graph of some function ,f, generate, when visualised, line segments, whence "flow lines" and "vector fields".
Higher dimensional problems arise very natural and the concepts of direction and magnitude, defined via a scalar product, can be used there as well.
Solving linear systems or linear optimization in $n$ variables are nice appplications.