# Consider the vector v between (-4,-4,-4) and (6,7,1). What vector has the same direction as vector v, but has length 3?

*print*Print*list*Cite

Expert Answers

mlehuzzah | Certified Educator

The vector being described here is <10,11,5>

6-(-4)=10, 7-(-4)=11, 1-(-4)=5

Its length is:

`sqrt(10^2+11^2+5^2)=sqrt(100+121+25)=sqrt(246)~~15.6843871`

We want a vector in the same direction, so we multiply each entry by the same positive number. We want the length to go from 15.68 to 3, so we multiply by `3/sqrt(246)~~.191273014`

Thus, the vector we want is

`<30/sqrt(246),33/sqrt(246),15/sqrt(246)>`