What is the cross product of $[2, - 1, 1]$ $[2, -1, 1]$ and $[3, - 6, 4]$ $[3,-6,4]$ ?

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Answer 1 · 2018-04-19T06:25:43

The vector is $= ⟨ 2, - 5, - 9 ⟩$ $=〈2,-5,-9〉$

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 $veca=〈2,-1,1〉$ and $vecb=〈3,-6,4〉$

Therefore,

$| (veci,vecj,veck), (2,-1,1), (3,-6,4) |$

$=veci| (-1,1), (-6,4) | -vecj| (2,1), (3,4) | +veck| (2,-1), (3,-6) |$

$=veci((-1)*(4)-(-6)*(1))-vecj((2)*(4)-(1)*(3))+veck((2)*(-6)-(-1)*(3))$

$=〈2,-5,-9〉=vecc$

Verification by doing 2 dot products

$〈2,-5,-9〉.〈2,-1,1〉=(2)*(2)+(-5)*(-1)+(-9)*(1)=0$

$〈2,-5,-9〉.〈3,-6,4〉=(2)*(3)+(-5)*(-6)+(-9)*(4)=0$

So,

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

What is the cross product of [2, -1, 1][2,−1,1][2, -1, 1] and [3,-6,4] [3,−6,4][3,-6,4] ?