How do you normalize (- 7 i -j -25k)?

May 2, 2017

$\frac{1}{15 \sqrt{3}} \left(- 7 \hat{i} - \hat{j} - 25 \hat{k}\right)$

Explanation:

A normalised vector is just the vector divided by its metric norm, so that the norm of the new scaled vector is unity:

Let:

$\vec{u} = - 7 \hat{i} - \hat{j} - 25 \hat{k}$

So the metric norm is given by:

$| | \overline{u} | {|}^{2} = {\left(- 7\right)}^{2} + {\left(- 1\right)}^{2} + {\left(- 25\right)}^{2}$
$\text{ } = 49 + 1 + 625$
$\text{ } = 675$

$\therefore | | \overline{u} | | = 15 \sqrt{3}$

And so:

$\hat{\overline{u}} = \frac{\overline{u}}{| | \overline{u} | |}$
$\setminus \setminus = \frac{\overline{u}}{15 \sqrt{3}}$
$\setminus \setminus = \frac{1}{15 \sqrt{3}} \left(- 7 \hat{i} - \hat{j} - 25 \hat{k}\right)$