# What is the cross product of [4, 0, 1] and [-1, 2, 3] ?

Feb 4, 2016

$A X B = - 2 i - 13 j + 8 k$
$A = 4 i + 0 j + 1 k$
$B = - 1 i + 2 j + 3 k$
$A X B = i \left({A}_{j} {B}_{k} - {A}_{k} {B}_{j}\right) - j \left({A}_{i} {B}_{k} - {A}_{k} {B}_{i}\right) + k \left({A}_{i} {B}_{j} - {A}_{J} {B}_{i}\right)$
$A X B = i \left(0 \cdot 3 - 1 \cdot 2\right) - j \left(4 \cdot 3 + 1 \cdot 1\right) + k \left(4 \cdot 2 + 0 \cdot 1\right)$
$A X B = i \left(- 2\right) - j \left(13\right) + k \left(8\right)$
$A X B = - 2 i - 13 j + 8 k$