How do you normalize #<0, 1, 3>#?
1 Answer
Aug 7, 2017
Explanation:
Normalization of a vector is the process of finding a unit vector in the same direction of that vector (with magnitude (or "norm")
#ulbar(|stackrel(" ")(" "hatv = (vecv)/(||vecv||)" ")|)#
where
#hatv# denotes the unit vector
#||vecv||# is the magnitude of vector#vecv#
The magnitude of
#||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) >" ")|)#