# What is the cross product of <7 ,4 ,1 > and <-5 ,2 ,8 >?

Jun 26, 2016

Cross product is $< 30 , - 61 , 34 >$

#### Explanation:

Cross product of $< {a}_{1} , {a}_{2} , {a}_{3} >$ and $< {b}_{1} , {b}_{2} , {b}_{3} >$ is

$< \left({a}_{2} \cdot {b}_{3} - {a}_{3} \cdot {b}_{2}\right) , \left({a}_{3} \cdot {b}_{1} - {a}_{1} \cdot {b}_{3}\right) , \left({a}_{1} \cdot {b}_{2} - {a}_{2} \cdot {b}_{1}\right) >$

Hence cross product of $< 7 , 4 , 1 >$ and $< - 5 , 2 , 8 >$

is $< \left(4 \cdot 8 - 1 \cdot 2\right) , \left(1 \cdot \left(- 5\right) - 7 \cdot 8\right) , \left(7 \cdot 2 - 4 \cdot \left(- 5\right)\right) >$

i.e. $< \left(32 - 2\right) , \left(- 5 - 56\right) , \left(14 + 20\right) >$

or $< 30 , - 61 , 34 >$