How do you normalize #(- 4i + 5 j- k)#?

1 Answer
Apr 30, 2017

Answer:

# -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#