What is the cross product of $[1, 3, 4]$ $[1, 3, 4]$ and $[3, 7, 9]$ $[3, 7, 9]$ ?

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Answer 1 · 2017-04-11T11:24:02

The vector is $= ⟨ - 1, 3, - 2 ⟩$ $=〈-1,3,-2〉$

The cross product of 2 vectors is

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

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

Here, we have $veca=〈1,3,4〉$ and $vecb=〈3,7,9〉$

Therefore,

$| (veci,vecj,veck), (1,3,4), (3,7,9) |$

$=veci| (3,4), (7,9) | -vecj| (1,4), (3,9) | +veck| (1,3), (3,7) |$

$=veci(3*9-4*7)-vecj(1*9-4*3)+veck(1*7-3*3)$

$=〈-1,3,-2〉=vecc$

Verification by doing 2 dot products

$〈-1,3,-2〉.〈1,3,4〉=-1*1+3*3-2*4=0$

$〈-1,3,-2〉.〈3,7,9〉=-1*3+3*7-2*9=0$

So,

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

What is the cross product of [1, 3, 4][1,3,4][1, 3, 4] and [3, 7, 9][3,7,9][3, 7, 9]?