What is the cross product of $[3, 0, 5]$ and $[2, -1, 1]$ ?

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Answer 1 · 2018-04-10T06:36:30

The vector is $=〈5,7,-3〉$

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 $veca=〈3,0,5〉$ and $vecb=〈2,-1,1〉$

Therefore,

$| (veci,vecj,veck), (3,0,5), (2,-1,1) |$

$=veci| (0,5), (-1,1) | -vecj| (3,5), (2,1) | +veck| (3,0), (2,-1) |$

$=veci((0)*(1)-(-1)*(5))-vecj((3)*(1)-(2)*(5))+veck((3)*(-1)-(0)*(2))$

$=〈5,7,-3〉=vecc$

Verification by doing 2 dot products

$〈5,7,-3〉.〈3,0,5〉=(5)*(3)+(7)*(0)+(-3)*(5)=0$

$〈5,7,-3〉.〈2,-1,1〉=(5)*(2)+(7)*(-1)+(-3)*(1)=0$

So,

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

What is the cross product of [3, 0, 5][3, 0, 5] and [2, -1, 1] [2, -1, 1] ?