# What is the cross product of <7, 5 ,6 > and <3 ,5 ,-2 >?

$- 4 \left(10 \hat{i} - 8 \hat{j} - 5 \hat{k}\right)$.
Let us consider $\vec{A} = \left(7 , 5 , 6\right) , \vec{B} = \left(3 , 5 , - 2\right)$ as $\vec{A} = 7 \hat{i} + 5 \hat{j} + 6 \hat{k}$, $\vec{B} = 3 \hat{i} + 5 \hat{j} - 2 \hat{k}$
$\vec{A} \times \vec{B} = \hat{i} \left(- 10 - 30\right) - \hat{j} \left(- 14 - 18\right) + \hat{k} \left(35 - 15\right)$
$\implies - 40 \hat{i} + 32 \hat{j} + 20 \hat{k}$
$\therefore \vec{A} \times \vec{B} = - 4 \left(10 \hat{i} - 8 \hat{j} - 5 \hat{k}\right)$.