How would you find a unit vector in the direction v = 6i-2j?

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Answer 1 · 2016-10-19T12:41:26

$vec(hatv)=(sqrt10/10)(3veci-vecj)$

A unit vector $vec(hatx)$ in the direction of $vecx$ is given by

$vec(hatx)=vecx/|x|$

In this case we have:

$|v|=sqrt(6^2+2^2)=sqrt40=2sqrt10$

So a unit vector in the direction of $vecv$

$vec(hatv)=(1/(2sqrt10))(6veci-2vecj)=(1/sqrt10)(3veci-vecj)$

Rationalizing the denominator we end up with

$vec(hatv)=(sqrt10/10)(3veci-vecj)$