Question

given v=i-2j find the unit vector

Answer 1

find the length of v by first finding the magnitude squared using the dot product:
\[ | \vec{v} |^2 = \vec{v} \dot\, \vec{v}\]
and then divide each component of v by this magnitude. the new vector will have unit length. (As a test, find the dot product with itself... you will get 1)