Unit Vector Question

Question

Find the unit vector that has the same direction as the vector v.

v=-24i-7j

Answer 1

v =<-24,7>

unit vector = v/25 =<-24i/25, 7j/25>

the i and j components form two legs of a right triangle with hypotenuse = 25

(-24)^2 + 7^2 = 25^2

576 + 49 = 625

divide the hypotenuse by 25 to get 1, the unit vector

also divide the two legs by 25

dilate the triangle by a factor of 1/25