How do you find the cross product and verify that the resulting vectors are perpendicular to the given vectors $<-3,-1,2>times<4,-4,0>$ ?

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Answer 1 · 2016-10-28T11:35:43

The cross product $〈8,8,16〉$

The cross product of 2 vectors $vecu=〈u_1,u_2,u_3〉$ and $vecv=〈v_1,v_2,v_3〉$ is given by

$vecu$ x $vecv$ $=〈u_2v_3-u_3v_2,u_3v_1-u_1v_3,u_1v_2-u_2v_1〉$
This vector is perpendicular to $vecu$ and $vecv$

So the cross product of $〈-3,-1,2〉$ and $〈4,-4,0〉$ is $〈8,8,16〉$

Verification by making the dot product
$〈-3,-1,2〉.〈8,8,16〉=-24-8+32=0$
and $〈4,-4,0〉.〈8,8,16〉=32-32+0=0$

As both dot products are $=0$ so the vector is perpendicular to the other 2 vectors

How do you find the cross product and verify that the resulting vectors are perpendicular to the given vectors <-3,-1,2>times<4,-4,0><-3,-1,2>times<4,-4,0>?