How do you normalize <0,2,0>?

1 Answer
May 21, 2016

Answer:

Normalizing a vector involves dividing each of its elements by the length of the vector, so that we end up with a vector of unit length in the same direction as the original vector. In this case #<0,1,0>#.

Explanation:

First find the length of the original vector:

#l=sqrt(0^2+2^2+0^2)=sqrt4=2#

Now divide each element by this length, and the normalised vector is #<0/2,2/2, 0/2> = <0,1,0>#

This makes sense: our original vector was of length 2 in the #x# (or (#j#) direction, and the normalised vector is in the same direction and of length #1# unit.