# What is the cross product of [1, -4, 0] and [4,3,6] ?

Jun 1, 2016

It is $\left(- 24 , - 6 , 19\right)$.

#### Explanation:

The cross product of two vectors with coordinates

${v}_{1} = \left({x}_{1} , {y}_{1} , {z}_{1}\right)$
${v}_{2} = \left({x}_{2} , {y}_{2} , {z}_{2}\right)$

is defined as

${v}_{1} \setminus \times {v}_{2} = \left({y}_{1} {z}_{2} - {z}_{1} {y}_{2} , {z}_{1} {x}_{2} - {x}_{1} {z}_{2} , {x}_{1} {y}_{2} - {y}_{1} {x}_{2}\right)$

We can apply this to our case

${v}_{1} = \left(1 , - 4 , 0\right)$
${v}_{2} = \left(4 , 3 , 6\right)$

${v}_{1} \setminus \times {v}_{2} = \left(- 4 \cdot 6 - 0 \cdot 3 , 0 \cdot 4 - 1 \cdot 6 , 1 \cdot 3 - \left(- 4\right) \cdot 4\right)$
$= \left(- 24 , - 6 , 19\right)$.