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

Oct 18, 2015

The vector you are looking for is v=[-24/sqrt(177);21/sqrt(177);24/sqrt(177)]

#### Explanation:

If you multiply all coordinates of a vector by a positive constant the length of the vector will also be multiplied by this constant, so the way to change the length of a vector is
1) calculate the length of the original vector
2) divide the vector by its length. (the new vector will have the length of $1$)
3) multiply the vector you got in 2) by the new length .