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The Magnitude of a Vector

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is also referred to as its magnitude.

The magnitude of a vector is the distance from the tail to the head of the vector. It is represented as |Vj and is equal to -\j x2+y2

It is very useful to scale a vector so that the resultant vector has a length of 1, with the same direction as the original vector. This process is called normalizing a vector. The resultant vector is called a unit vector. To normalize a vector V, we simply scale it by the value l/|Vj. The resultant unit vector is represented as V=V/jV|. r y -i

Interestingly, a unit vector along the x-axis is quite simply the vector ^

Unit Vector

Unit Vector

V=V/ IVI Fig. 2.5: A Unit Vector and a unit vector along the the y axis is