# How do you normalize  (-300i + 200j - 150k)?

Apr 28, 2016

The normalised vector is: $\left(\left(- \frac{300}{390.5}\right) i + \left(\frac{200}{390.5}\right) j - \left(\frac{150}{390.5}\right) k\right)$, which can also be expressed as $\left(- 0.77 i + 0.51 j - 0.38 k\right)$

#### Explanation:

Normalising a vector involves dividing each of its elements by the length of the vector. This yields a vector in the same direction as the original vector, but one unit in length.

First we find the length of the vector:

$l = \sqrt{{\left(- 300\right)}^{2} + {200}^{2} + {\left(- 150\right)}^{2}} = \sqrt{90000 + 40000 + 22500}$
$= \sqrt{152500} \approx 390.5$ $u n i t s$

The normalised vector, then, is:

$\left(\left(- \frac{300}{390.5}\right) i + \left(\frac{200}{390.5}\right) j - \left(\frac{150}{390.5}\right) k\right)$