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 (pronounced "v-hat"). For example, the vector has magnitude . It's unit vector is given by the following: Figure 2-6 shows that 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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Figure 2-6.

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.

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