How do you normalize (- 4i + 5 j- k)?
1 Answer
Apr 30, 2017
-4/sqrt(42)hati+5/ sqrt(42)hatj-1/ sqrt(42)hatk
Explanation:
A normalised vector is just the vector divided by its metric norm, so that the norm of the new scaled vector is unity:
Let:
vec u = -4hati+5hatj-hatk
So the metric norm is given by:
|| bar u || ^2 = (-4)^2+(5)^2+(-1)^2
" " = 16+25+1
" " = 42
:. || bar u || = sqrt(42)
And so:
hatbaru = (baru) / (|| bar u ||)
\ \ = (baru) / sqrt(42)
\ \ = 1 / sqrt(42) (-4hati+5hatj-hatk
\ \ = -4/ sqrt(42)hati+5/ sqrt(42)hatj-1/ sqrt(42)hatk
