What is the cross product of $[1, 3, 4]$ $[1, 3, 4]$ and $[2, - 5, 8]$ $[2, -5, 8]$ ?

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Answer 1 · 2017-03-08T15:46:39

The vector is $= ⟨ 44, 0, - 11 ⟩$ $=〈44,0,-11〉$

The vector perpendicular to 2 vectors is calculated with the determinant (cross product)

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

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

Here, we have $veca=〈1,3,4〉$ and $vecb=〈2,-5,8〉$

Therefore,

$| (veci,vecj,veck), (1,3,4), (2,-5,8) |$

$=veci| (3,4), (-5,8) | -vecj| (1,4), (2,8) | +veck| (1,3), (2,-5) |$

$=veci(44)-vecj(0)+veck(-11)$

$=〈44,0,-11〉=vecc$

Verification by doing 2 dot products

$veca.vecc$

$=〈1,3,4>.〈44,0,-11〉=44-44=0$

$vecb.vecc$

$=〈2,-5,8〉.〈44,0,-11〉=88-88=0$

So,

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

What is the cross product of [1, 3, 4][1,3,4][1, 3, 4] and [2, -5, 8] [2,−5,8][2, -5, 8] ?