What is the cross product of $[1, - 2, - 3]$ $[1, -2, -3]$ and $[3, 7, 9]$ $[3, 7, 9]$ ?

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Answer 1 · 2018-03-24T13:20:44

The vector is $= ⟨ 3, - 18, 13 ⟩$ $=〈3,-18,13〉$

The cross product of 2 vectors is calculated with the determinant

$| (veci,vecj,veck), (d,e,f), (g,h,i) |$

where $veca=〈d,e,f〉$ and $vecb=〈g,h,i〉$ are the 2 vectors

Here, we have $veca=〈1,-2,-3〉$ and $vecb=〈3,7,9〉$

Therefore,

$| (veci,vecj,veck), (1,-2,-3), (3,7,9) |$

$=veci| (-2,-3), (7,9) | -vecj| (1,-3), (3,9) | +veck| (1,-2), (3,7) |$

$=veci((-2)*(9)-(-3)*(7))-vecj((1)*(9)-(-3)*(3))+veck((1)*(7)-(-2)*(3))$

$=〈3,-18,13〉=vecc$

Verification by doing 2 dot products

$〈3,-18,13〉.〈1,-2,-3〉=(3)*(1)+(-18)*(-2)+(13)*(-3)=0$

$〈3,-18,13〉.〈3,7,9〉=(3)*(3)+(-18)*(7)+(13)*(9)=0$

So,

$vecc$ is perpendicular to $veca$ and $vecb$

What is the cross product of [1, -2, -3][1,−2,−3][1, -2, -3] and [3, 7, 9][3,7,9][3, 7, 9]?