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

Question

9543 views around the world

You can reuse this answer
Creative Commons License

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)#