How to find a vector A that has the same direction as ⟨−8,7,8⟩ but has length 3 ?
The vector you are looking for is
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
3) multiply the vector you got in 2) by the new length .