How do you normalize 3i+7j-2k?

1 Answer
Aug 28, 2017

Answer:

The unit vector is #=3/sqrt62hati+7/sqrt62hatj-2/sqrt62hatk#

Explanation:

Let #veca =3hati+7hatj-2hatk= <3,7,-2>#

The magnitude of #veca# is

#||vecaa||=||3,7,-2||=sqrt(3^2+7^2+(-2)^2)=sqrt(9+49+4)#

#=sqrt(62)#

Therefore,

#hata=veca/(||veca||)=1/sqrt62<3,7,-2> #

#= <3/sqrt62,7/sqrt62,-2/sqrt62>#

Verification

#||hata||=sqrt((3/sqrt62)^2+(7/sqrt62)^2+(-2/sqrt62)^2)#

#=sqrt(9/62+49/62+4/62)=sqrt(62/62)=1#