# How do you normalize  (18i -30j -12k) ?

May 26, 2016

#### Answer:

Normalising a vector involves dividing each of its elements by its length, to yield a new vector of length 1 unit in the same direction as the original vector. In this case, the length of the vector is $37$ units so the normalised vector is $\left(\frac{18}{37} i - \frac{30}{37} j - \frac{12}{37} k\right)$.

#### Explanation:

Length of the vector:

$l = \sqrt{{18}^{2} + {\left(- 30\right)}^{2} + {\left(- 12\right)}^{2}} = \sqrt{324 + 900 + 144} = \sqrt{1368} \approx 37$