Find a vector 10 units long in the direction of u = 3i + 3j.
first let's find the unit vector in this direction.
let v be the unit vector in the direction of u
=> v = u/|u|
|u| = sqrt(3^2 + 3^2) = sqrt(18)
=> v = <3/sqrt(18), 3/sqrt(18)>
so to get a vector 10 units long, we just multiply the unit vector by 10
=> x = <30/sqrt(18), 30/sqrt(18)> = [30/sqrt(18)]i + [30/sqrt(18)]j