How do you find the unit vector in the direction of the given vector of #v=i+j#?

Question

8048 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-11T13:54:27

#hatvecv=sqrt2/2(hatveci+hatvecj)#

By definition a unit vector has a magnitude (modulus) of 1. So to find a unit vector of any given vector in that direction we work out:

#hatvecv=vecv/|vecv|#

in this case

#vecv=hatveci+hatvecj#

#|vecv|=sqrt(1^2+1^2)=sqrt2#

#hatvecv=1/sqrt2(hatveci+hatvecj)#

#hatvecv=sqrt2/2(hatveci+hatvecj)#