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

#### Risposta:

(-24/sqrt(177),21/sqrt(177),24/sqrt(177))

#### Spiegazione:

The idea is based on a concept of scaling and similarity.
Any vector that "has the same direction" as (-8,7,8) has all the coordinates proportional to this given vector and, therefore, can be described by coordinates (-8f,7f,8f) where f is a scaling factor.

All we need now is to find a scaling factor that leads to a vector with the length 3.

The length of a vector with coordinates (-8f,7f,8f) uguale a
sqrt(64f^2+49f^2+64f^2) = f*sqrt(177)

So, if we want the length to be equal to 3, we should choose
f = 3/sqrt(177)

The coordinates of a vector with the same direction as (-8,7,8) but with the length 3 sarà
(-24/sqrt(177),21/sqrt(177),24/sqrt(177))