How do you normalize #<-3,0,1>#?

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Answer 1 · 2017-01-24T09:01:16

See explanation.

To normalize a vector you have to divide all vector's coordinates by the vector's norm.

#||v||=sqrt(x^2+y^2+z^2)#

Here we have:

#||v||=sqrt((-3)^2+0^2+1^2)=sqrt(9+1)=sqrt(10)#

So the normalized vector is:

#v_1=<-3/sqrt(10),0,1/sqrt(10)>#

After rationalizing the denomionators you get:

#v_1=<-(3sqrt(10))/10,0,sqrt(10)/10>#