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

1 Answer
Mr. Lacine
Feb 16, 2018

The unit vector of v=<5/13, -12/13>v=<513,−1213>.

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)v=<x,y>,mag.ofv=√x2+y2.
Using the formulas together you get, magnitude of v= sqrt(5^2+(-12)^2)= 13√52+(−12)2=13 as 5, 12, 13 are a pythagorean triple. Dividing vector v by its magnitude results in: unit vector = v*1/13v⋅113 = <5/13,-12/13><513,−1213>.

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