# What is the cross product of (4 i + 4 j + 2 k) and (- 4 i - 5 j + 2 k)?

Feb 17, 2016

$A X B = 18 i - 16 j$

#### Explanation:

$A = \left(x , y , z\right)$
$B = \left(a , b , c\right)$
$A X B = i \left(y \cdot c - z \cdot b\right) - j \left(x \cdot c - z \cdot a\right) + k \left(x \cdot b - y \cdot a\right)$
$A = 4 i + 4 j + 2 k$
$B = - 4 i - 5 j + 2 k$
$A X B = i \left(8 + 10\right) - j \left(8 + 8\right) + k \left(- 20 + 20\right)$
$A X B = 18 i - 16 j + 0$
$A X B = 18 i - 16 j$