]> 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.