How do you find a unit vector that has the same direction as the given vector 5i + 9j?

Divide each term by the magnitude of the vector to get:
##color(white)(XXX)##unit vector: ##color(green)(-5/sqrt(106)i+9/sqrt(106)j)##
Using the Pythagorean Theorem:
##color(white)(XXX)abs(-5i+9j) =sqrt((-5)^2+9^2)=sqrt(25+81)=sqrt(106)##