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We will call a sequence of numbers of length k a k-vector.
We define addition and subtraction among vectors of
the same length 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 that space by a vector
whose first component is the x coordinate of the point and
second is the y component, that is, by
(x, y).
We call the vector with i-th component value =1 and
the rest 0 the basis vector in the ith direction. In ordinary
three dimensional space the basis vectors in the z y and z
directions are denoted as i, j and k respectively.
The vector (x, y, z) can also be written as xi+
yj + zk.
We assume here that basis vectors are perpendicular to one
another, and each has unit length.
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