What is || <1, 6, -3 > - < 4, -2, -9 >||?

Apr 13, 2017

$| | \left\langle1 , 6 , - 3\right\rangle - \left\langle4 , - 2 , - 9\right\rangle | | = \sqrt{109}$

Explanation:

Let:

$\vec{u} = \left\langle1 , 6 , - 3\right\rangle - \left\langle4 , - 2 , - 9\right\rangle$

First we will simplify the vector:

$\vec{u} = \left\langle\left(1\right) - \left(4\right) , \left(6\right) - \left(- 2\right) , \left(- 3\right) - \left(- 9\right)\right\rangle$
$\text{ } = \left\langle- 3 , 8 , 6\right\rangle$

Then we compute the norm:

$| | \vec{u} | | = \sqrt{{\left(- 3\right)}^{2} + {\left(8\right)}^{2} + {\left(6\right)}^{2}}$
$\text{ } = \sqrt{9 + 64 + 36}$
$\text{ } = \sqrt{109}$