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

Feb 2, 2016

#### Answer:

$A X B = 4 i - 10 j - 18 k$

#### Explanation:

$A = i + 4 j - 2 k$
$B = 3 i - 6 j + 4 k$
$A X B = i \left(\left(A j \cdot B k\right) - \left(A k \cdot B j\right)\right) - j \left(\left(A i \cdot B k\right) - \left(A k \cdot B i\right)\right) + k \left(\left(A i \cdot B j\right) - \left(A j \cdot B i\right)\right)$
A X B=i(4*4-((-2)*(-6)))-j(1*4-(3*(-2))+k(1*(-6)-(3*4))
$A X B = i \left(16 - 12\right) - j \left(4 + 6\right) + k \left(- 6 - 12\right)$
$A X B = i \left(4\right) - j \left(10\right) + k \left(- 18\right)$
$A X B = 4 i - 10 j - 18 k$