I do not understand something about cross products. Say,(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \vec A\times \vec B=\vec C=(C_x, C_y, C_z) [/tex]

and,

[tex] \vec C=(A_x \hat x+A_y \hat y+A_z \hat z)\times (B_x \hat x+B_y \hat y+B_z \hat z)[/tex]

but why is this equivalent to

[tex] (A_x B_y - A_y B_x)\hat x \times \hat y + (A_x B_z - A_z B_x) \hat x \times \hat z + (A_y B_z - A_z B_y) \hat y \times \hat z [/tex]

?????

Can someone show me how do i get this? Preferbly an algebraic method instead of a geometric one, because I am poor at visualizing stuff.

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# A cross product question.

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