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

1 Answer
Aug 7, 2017

Answer:

#hatv = < 0, 1/(sqrt10), 3/(sqrt10) >#

Explanation:

Normalization of a vector is the process of finding a unit vector in the same direction of that vector (with magnitude (or "norm") #1#). It is found by the equation

#ulbar(|stackrel(" ")(" "hatv = (vecv)/(||vecv||)" ")|)#

where

#hatv# denotes the unit vector

#||vecv||# is the magnitude of vector #vecv#

The magnitude of #vecv# is given by

#||vecv|| = sqrt(0^2 + 1^2 + 3^2) = color(red)(ul(sqrt10#

Thus, we have

#hatv = (< 0,1,3 >)/(color(red)(sqrt10)) = color(blue)(ulbar(|stackrel(" ")(" "< 0, 1/(sqrt10), 3/(sqrt10) >" ")|)#