# What is the cross product of [4, -4, 4] and [5, 2, -2] ?

Feb 8, 2016

$P X Q = 28 j - 12 k$
P(a,b,c); Q(d,e,f)
$P X Q = i \left(b \cdot f - c \cdot e\right) - j \left(a \cdot f - c \cdot d\right) + k \left(a \cdot e - b \cdot d\right)$
$\left(4 , - 4 , 4\right) X \left(5 , 2 , - 2\right) = i \left(8 - 8\right) - j \left(- 28\right) + k \left(- 12\right)$
$P X Q = 28 j - 12 k$