How do you find two unit vectors parallel to vector a= [-4, -1, -6]?

Jun 19, 2018

$\left(\frac{4}{\sqrt{53}} , \frac{1}{\sqrt{53}} , \frac{6}{\sqrt{53}}\right)$ and $\left(- \frac{4}{\sqrt{53}} , - \frac{1}{\sqrt{53}} , - \frac{6}{\sqrt{53}}\right)$

Explanation:

Consider the vector defined by $\pm \frac{\vec{a}}{|} | \vec{a} | |$, where, $| | \vec{a} | |$ is the

magnitude of $\vec{a} \ne \vec{0}$.

Here, $| | \vec{a} | | = \sqrt{{\left(- 4\right)}^{2} + {\left(- 1\right)}^{2} + {\left(- 6\right)}^{2}} = \sqrt{53}$.

So, $\left(\frac{4}{\sqrt{53}} , \frac{1}{\sqrt{53}} , \frac{6}{\sqrt{53}}\right)$ and $\left(- \frac{4}{\sqrt{53}} , - \frac{1}{\sqrt{53}} , - \frac{6}{\sqrt{53}}\right)$

are the desired vectors.