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

To normalise a vector we divide each of its elements by the length of the vector. First find the length: $r = \sqrt{{\left(- 3\right)}^{2} + {1}^{2} + {\left(- 1\right)}^{2}} = \sqrt{11} \approx 3.3$. The normalised vector can be written as $\left(\frac{- 3}{\sqrt{11}} i + \frac{1}{\sqrt{11}} j - \frac{1}{\sqrt{11}} k\right)$ or $\left(- \frac{3}{3.3} i + \frac{1}{3.3} j - \frac{1}{3.3} k\right)$.