# What is || <7, 3, -1> - < -2 , 5, 3 > ||?

Jan 10, 2017

$| | < 7 , 3 , - 1 > - < - 2 , 5 , 3 > | | = \sqrt{101}$.

See below.

#### Explanation:

To subtract two vectors $\vec{a}$ and $\vec{b}$:

$\vec{a} - \vec{b} = < {a}_{1} - {b}_{1} , {a}_{2} - {b}_{2} , {a}_{3} - {b}_{3} >$

The result is a vector, $\vec{c}$.

The magnitude of the resultant vector is then given by:

$| \vec{c} | = \sqrt{{\left({c}_{1}\right)}^{2} + {\left({c}_{2}\right)}^{2} + {\left({c}_{3}\right)}^{2}}$

Given $\vec{a} = < 7 , 3 , - 1 >$ and $\vec{b} = < - 2 , 5 , 3 >$,

$\vec{a} - \vec{b} = < 7 - \left(- 2\right) , 3 - 5 , - 1 - 3 >$

$= < 9 , - 2 , - 4 >$

The magnitude is then:

$| \vec{c} | = \sqrt{{9}^{2} + {\left(- 2\right)}^{2} + {\left(- 4\right)}^{2}}$

$= \sqrt{101}$