Question

How do you find the unit vector in the direction of the given vector of `v=<5,-12>`?

Answer 1

The unit vector of `v=<5/13, -12/13>`.

Explanation:

Unit vector formula is the vector divided by its magnitude. The formula for magnitude is: given `v=<x,y>, mag. of v= sqrt(x^2+y^2)`.
Using the formulas together you get, magnitude of v= `sqrt(5^2+(-12)^2)= 13` as 5, 12, 13 are a pythagorean triple. Dividing vector v by its magnitude results in: unit vector = `v*1/13` = `<5/13,-12/13>`.