# What is the cross product of [-3, 5, -3] and [4, -11, 11] ?

Mar 1, 2016

$\vec{C} = 22 i + 21 j + 13 k$

#### Explanation:

$\text{the cross product of two vector is given as :}$
$\vec{A} = \left(a , b , c\right)$
$\vec{B} = \left(d , e , f\right)$
$\vec{C} = \vec{A} X \vec{B}$
$\vec{C} = i \left(b \cdot f - c \cdot e\right) - j \left(a \cdot f - c \cdot d\right) + k \left(a \cdot e - b \cdot d\right)$
$\text{Thus:}$
$\vec{C} = i \left(5 \cdot 11 - 11 \cdot 3\right) - j \left(- 3 \cdot 11 - \left(- 3 \cdot 4\right)\right) + k \left(\left(- 3\right) \cdot \left(- 11\right) - 5 \cdot 4\right)$
$\vec{C} = i \left(55 - 33\right) - j \left(- 33 + 12\right) + k \left(33 - 20\right)$
$\vec{C} = 22 i + 21 j + 13 k$