Math Help - vector

Find a vector 10 units long in the direction of u = 3i + 3j.


Thanks

Originally Posted by Mr_Green

Find a vector 10 units long in the direction of u = 3i + 3j.


Thanks

let the vector we are looking for be x

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