School of Mathematics and Statistics, The University of Sydney
 4. Multiplication of a vector by a scalar
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Unit vectors and how to get them

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It is often useful to be able to find a unit vector (a vector of length 1) in the direction of a given non-zero vector v. A common notation used for this unit vector is v^.

For example, if v has length 3, then v^ = 1 3v has length 1 and is in the same direction as v.

              v 1 --v 3

In general, the unit vector in the same direction as v is

^v =  v-.      |v |

Since ^v = v- |v|, we also have v = |v|^v.

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