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

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Answer 1 · 2017-07-31T09:36:41

The vector is $= ⟨ - 7, - 4, 1 ⟩$ $=〈-7,-4,1〉$

The cross product of 2 vectors is calculated with the determinant

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

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

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

Therefore,

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

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

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

$=〈-7,-4,1〉=vecc$

Verification by doing 2 dot products

$〈1,-2,-1〉.〈-7,-4,1〉=-7*1+2*4-1*1=0$

$〈1,-2,-1〉.〈1,-1,3〉=1*1+1*2-1*3=0$

So,

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

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