What is the cross product of $[3,2, 5]$ and $[1,2,-4]$ ?

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What is the cross product of $[3,2, 5]$ and $[1,2,-4]$ ?

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Answer 1 · 2016-10-27T18:41:28

The cross product is $=〈-18,17,4〉$

Explanation:

Let the vectors be $veca=〈a_1,a_2,a_3〉$ and $vecb=〈b_1,b_2,b_3〉$

The cross product is given by
$veci$ $color(white)(aaaa)$ $vecj$ $color(white)(aaaa)$ $veck$
$a_1$ $color(white)(aaaaa)$ $a_2$ $color(white)(aaaa)$ $a_3$
$b_1$ $color(white)(aaaaa)$ $b_2$ $color(white)(aaaa)$ $b_3$

$=〈a_2b_3-a_3b_2,a_3b_1-a_1b_3,a_1b_2-a_2b_1〉$

With the vectors $〈3,2,5〉$ and $〈1,2,-4〉$
we get the cross product $〈-8-10,12+5,6-2〉$
$=〈-18,17,4〉$

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What is the cross product of $[3,2, 5]$ and $[1,2,-4]$ ?

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Explanation:

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What is the cross product of $[3,2, 5]$ and $[1,2,-4]$ ?