]> 3.1 Vectors

3.1 Vectors

We will call a sequence of numbers of length $k$ a k-vector.

We define addition and subtraction among k-vectors to be termwise addition and subtraction, so that for 2-vectors we have

$( a , b ) + ( c , d ) = ( a + c , b + d )$

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 2-vector.

We call the vector with i-th component value = 1 and the rest 0 the basis vector in the i-th direction. In ordinary three dimensional space the basis vectors in the $x , y$ and $z$ directions are denoted as $i ^ , j ^$ and $k ^$ respectively. The vector $( x , y , z )$ can also be written as $x i ^ + y j ^ + z k ^$ .

We assume here that basis vectors are perpendicular to one another, and each has unit length.