How do you normalize $(- 7 i -j -25k)$ ?

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Answer 1 · 2017-05-02T01:57:41

$1 / (15sqrt(3)) (-7hati-hatj-25hatk)$

A normalised vector is just the vector divided by its metric norm, so that the norm of the new scaled vector is unity:

Let:

$vec u = -7hati-hatj-25hatk$

So the metric norm is given by:

$|| bar u || ^2 = (-7)^2+(-1)^2+(-25)^2$
$" " = 49+1+625$
$" " = 675$

$:. || bar u || = 15sqrt(3)$

And so:

$hatbaru = (baru) / (|| bar u ||)$
$\ \ = (baru) / (15sqrt(3))$
$\ \ = 1 / (15sqrt(3)) (-7hati-hatj-25hatk)$

How do you normalize (- 7 i -j -25k)(- 7 i -j -25k)?