How do you normalize # <2,3,1>#?

1 Answer
Mar 25, 2017

Answer:

#<<2/sqrt(14),3/sqrt(14),1/sqrt(14) >> #

Explanation:

To normalize a vector we calculate the vector norm (its magnitude) and scale the vector by dividing by the norm to create a unit vector.

So let:

# vec u = <<2,3,1, >> #

Then we calculate the vector norm:

# || vec u || = sqrt(2^2+3^2+1^2) #
# " " = sqrt(4+9+1) #
# " " = sqrt(14) #

Now we scale the initial vector by dividing by the norm to get:

# || hat u || = 1/sqrt(14) \ <<2,3,1, >> #

# " " = <<2/sqrt(14),3/sqrt(14),1/sqrt(14) >> #