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

1 Answer
Oct 19, 2016

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

Explanation:

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)#