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We will call a sequence of numbers of length a k-vector.
We define addition and subtraction among k-vectors to be termwise addition and subtraction, so that for 2-vectors 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 coordinate of the point and second is the component, that is, by , 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 and directions are denoted as and respectively. The vector can also be written as .
We assume here that basis vectors are perpendicular to one another, and each has unit length.
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