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

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Answer 1 · 2017-03-25T01:32:33

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

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:

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

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

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