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:

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