# What is || <1, 9, 7 > - < 2, -1, 2> ||?

Feb 5, 2016

$\sqrt{126}$

#### Explanation:

When adding or subtracting vectors in ${\mathbb{R}}^{n}$ we may simply add or subtract every component individually.

therefore(1,9,7)-(2,-1,2)=(1-2,9-(-1),7-2))

$= \left(- 1 , 10 , 5\right)$.

Now the norm of a vector in ${\mathbb{R}}^{n}$ may be found using the generalized Pythagoras Theorem, so in this case :

$| | \left(- 1 , 10 , 5\right) | | = \sqrt{{\left(- 1\right)}^{2} + {10}^{2} + {5}^{2}}$

$= \sqrt{126}$