What is the cross product of [9,4,-1] and [-1, -1, 2] ?

Feb 10, 2016

$A X B = 7 i - 17 j - 5 k$

Explanation:

$A = \left[{a}_{i} , {a}_{j} , {a}_{k}\right]$
$B = \left[{b}_{i} , {b}_{j} , {b}_{k}\right]$
$A X B = i \left({a}_{j} \cdot {b}_{k} - {a}_{k} \cdot {b}_{j}\right) - j \left({a}_{i} \cdot {b}_{k} - {a}_{k} \cdot {b}_{i}\right) + k \left({a}_{i} \cdot {b}_{j} - {a}_{j} \cdot {b}_{i}\right)$
thus;
$A = \left[9 , 4 , - 1\right]$
$B = \left[- 1 , - 1 , 2\right]$
$A X B = i \left(4 \cdot 2 - \left(- 1 \cdot - 1\right)\right) - j \left(9 \cdot 2 - \left(- 1 \cdot - 1\right)\right) + k \left(- 1 \cdot 9 - 4 \cdot - 1\right)$
$A X B = i \left(8 - 1\right) - j \left(18 - 1\right) + k \left(- 9 + 4\right)$
$A X B = 7 i - 17 j - 5 k$