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# 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)##