What is the cross product of $<9,2,8 >$ and $<6, -2, 7 >$ ?

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Answer 1 · 2018-03-06T13:40:58

The vector is $= <30,-15,-30>$

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 $veca=〈9,2,8〉$ and $vecb=〈6,-2,7〉$

Therefore,

$| (veci,vecj,veck), (9,2,8), (6,-2,7) |$

$=veci| (2,8), (-2,7) | -vecj| (9,8), (6,7) | +veck| (9,2), (6,-2) |$

$=veci((2)*(7)-(8)*(-2))-vecj((9)*(7)-(8)*(6))+veck((9)*(-2)-(2)*(6))$

$=〈30,-15,-30〉=vecc$

Verification by doing 2 dot products

$〈30,-15,-30〉.〈9,2,8〉=(30)*(9)+(-15)*(2)+(-30)*(8)=0$

$〈30,-15,-30〉.〈6,-2,7〉=(30)*(6)+(-15)*(-2)+(-30)*(7)=0$

So,

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

What is the cross product of <9,2,8 ><9,2,8 > and <6, -2, 7 ><6, -2, 7 >?