# What is the cross product of <5, 2 , 8 > and <4 ,7 ,3 >?

Feb 17, 2016

#< -50, 17, 27 >

#### Explanation:

The cross product of 2 vectors can be calculated as
$< {a}_{x} , {a}_{y} , {a}_{z} > \times < {b}_{x} , {b}_{y} , {b}_{z} > = < {c}_{x} , {x}_{y} , {c}_{z} >$
where $\left\{\begin{matrix}{c}_{x} = {a}_{y} {b}_{z} - {a}_{z} {b}_{y} \\ {c}_{y} = {a}_{z} {b}_{x} - {a}_{x} {b}_{z} \\ {c}_{z} = {a}_{x} {b}_{y} - {a}_{y} {b}_{x}\end{matrix}\right.$

Therefore:
$< 5 , 2 , 8 > \times < 4 , 7 , 3 >$

$\textcolor{w h i t e}{\text{XXX}} = < \left(2 \times 3 - 8 \times 7\right) , \left(8 \times 4 - 5 \times 3\right) , \left(5 \times 7 - 2 \times 4\right) >$

$\textcolor{w h i t e}{\text{XXX}} = < - 50 , 17 , 27 >$