The next operation that follows magnitude is normalization. Normalization consists of dividing every entry in a vector
by its magnitude to create a vector of length 1 known as the unit vector
For example, the vector
. It's unit vector is given by the following:
is made up of 6 unit vectors
. One can also easily see that normalization changes the magnitude to 1 but leaves the direction unchanged.
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Vector and its Unit Norm
An important application of normalization is to rescale a vector to a particular magnitude without changing its direction. If we take the same vector
above with magnitude 6 and want to give it a magnitude of 9 we simply multiply 9 by the unit vector
Find the norm of the vector
Find the vector in the same direction as
with magnitude 3.