Question

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

Answer 1

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)`

Explanation:

Using the Pythagorean Theorem:
`color(white)("XXX")abs(-5i+9j) =sqrt((-5)^2+9^2)=sqrt(25+81)=sqrt(106)`