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Magnitude and Unit Vectors

Vectors have a magnitude, usually depicted and thought about as length and written as NvN, meaning the magnitude of the vector v, where v is any vector. As with a line segment, the length or magnitude of a vector can be found using the distance formula. The distance formula is shown in Figure 1.16. A unit vector is simply a vector with a magnitude of one. Any vector can be converted into a unit vector using the process of normalization, by dividing the vector by the vector’s original magnitude. This is also shown in Figure 1.16.

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