# What is the cross product of <2 , 5 ,-3 > and <5 ,6 ,-2 >?

Feb 13, 2016

$A X B = < 8 , - 11 - 13 >$
$\left(a , b , c\right) X \left(d , e , f\right) = \left(b \cdot f - e \cdot c\right) - \left(a \cdot f - c \cdot d\right) + \left(a \cdot e - b \cdot d\right)$
$A = \left(2 , 5 , - 3\right) \text{ ;B=} \left(5 , 6 , - 2\right)$
$A X B = \left(5 \cdot \left(- 2\right) - \left(- 3 \cdot 6\right)\right) - \left(2 \cdot \left(- 2\right) - \left(- 3 \cdot 5\right)\right) + \left(2 \cdot 6 - 5 \cdot 5\right)$
$A X B = \left(- 10 + 18\right) - \left(- 4 + 15\right) + \left(12 - 25\right)$
$A X B = 8 i - 11 j - 13 k$
$A X B = < 8 , - 11 - 13 >$