
We will call a sequence of numbers of length $k$ a kvector.
We define addition and subtraction among kvectors to be termwise addition and subtraction, so that for 2vectors we have
If we choose an origin O in the Euclidean plane we can describe any point in the plane by a vector whose first component is the $x$ coordinate of the point and second is the $y$ component, that is, by $(x,y)$ , a 2vector.
We call the vector with ith component value = 1 and the rest 0 the basis vector in the ith direction. In ordinary three dimensional space the basis vectors in the $x,y$ and $z$ directions are denoted as $\widehat{i},\widehat{j}$ and $\widehat{k}$ respectively. The vector $(x,y,z)$ can also be written as $x\widehat{i}+y\widehat{j}+z\widehat{k}$ .
We assume here that basis vectors are perpendicular to one another, and each has unit length.
