# What is  || < 5 , -6 , 9> + < 2 , -4, -7 > || ?

May 24, 2017

$3 \sqrt{17}$

#### Explanation:

First, let us calculate the vector sum:

Let $\vec{u} \setminus = \left\langle5 , - 6 , 9\right\rangle$
And $\vec{v} = \left\langle2 , - 4 , - 7\right\rangle$

Then:

$\vec{u} + \vec{v} = \left\langle5 , - 6 , 9\right\rangle + \left\langle2 , - 4 , - 7\right\rangle$
$\text{ } = \left\langle\left(5\right) + \left(2\right) , \left(- 6\right) + \left(- 4\right) , \left(9\right) + \left(- 7\right)\right\rangle$
$\text{ } = \left\langle7 , - 10 , 2\right\rangle$

So then the metric norm is:

$| | \vec{u} + \vec{v} | | = | | \left\langle7 , - 10 , 2\right\rangle | |$
$\text{ } = \sqrt{{\left(7\right)}^{2} + {\left(- 10\right)}^{2} + {\left(2\right)}^{2}}$
$\text{ } = \sqrt{49 + 100 + 4}$
$\text{ } = \sqrt{153}$
$\text{ } = 3 \sqrt{17}$