How do you normalize  (5i- 3j + 12k) ?

Feb 20, 2016

Normalizing a vector creates a 'unit vector' 1 unit in length in the same direction as the original vector. In this case the normalized vector is $\left(\frac{5}{\sqrt{178}} i - \frac{3}{\sqrt{178}} j + \frac{12}{\sqrt{178}} k\right)$ or $\left(\frac{5}{13.3} i - \frac{3}{13.3} j + \frac{12}{13.3} k\right)$
The length of this vector is $l = \sqrt{{5}^{2} + {\left(- 3\right)}^{2} + {12}^{2}} = \sqrt{178} \approx 13.3$.
The normalized vector can be represented as $\left(\frac{5}{\sqrt{178}} i - \frac{3}{\sqrt{178}} j + \frac{12}{\sqrt{178}} k\right)$ or $\left(\frac{5}{13.3} i - \frac{3}{13.3} j + \frac{12}{13.3} k\right)$.