# What is the cross product of [1,-2,-1] and [4,3,6] ?

May 22, 2016

The cross product is $\left\{- 9 , - 10 , 11\right\}$.

#### Explanation:

For two vectors $\left\{a , b , c\right\}$ and $\left\{x , y , z\right\}$, the cross product is given by:

$\left\{\begin{matrix}b z - c y \\ c x - a z \\ a y - b x\end{matrix}\right\}$

In this case, the cross product is:

$\left\{\left(- 2 \cdot 6\right) - \left(- 1 \cdot 3\right) , \left(- 1 \cdot 4\right) - \left(1 \cdot 6\right) , \left(1 \cdot 3\right) - \left(- 2 \cdot 4\right)\right\}$

$= \left\{\left(- 12\right) - \left(- 3\right) , \left(- 4\right) - \left(6\right) , \left(3\right) - \left(- 8\right)\right\}$

$= \left\{- 9 , - 10 , 11\right\}$