# How to find a vector A that has the same direction as ⟨−8,7,8⟩ but has length 3 ?

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Let

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The idea is based on a concept of scaling and similarity.

Any vector that "has the same direction" as

All we need now is to find a scaling factor that leads to a vector with the length

The length of a vector with coordinates

So, if we want the length to be equal to

The coordinates of a vector with the same direction as

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