Find a unit vector that has the same direction as the given vector.

9i - j + 3k

√(9^2 + 1^2 + 3^2) = √91

unit vector = (9/√91) i - (1/√91)j + (3/√91)k

Just divide the vector by its own length:

(9i - j + 3k)/(sqrt(9^2 + (-1)^2 + 3^2))
= (9sqrt(91)/91)i - [sqrt(91)/91]j + (3sqrt(91)/91)k