What is the cross product of $<4 , 5 ,-9 >$ and $<4, 3 ,-3 >$ ?

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Answer 1 · 2018-03-18T10:26:38

The vector is $<12, -24, -8>$

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 $veca=〈4,5,-9〉$ and $vecb=〈4,3,-3〉$

Therefore,

$| (veci,vecj,veck), (4,5,-9), (4,3,-3) |$

$=veci| (5,-9), (3,-3) | -vecj| (4,-9), (4,-3) | +veck| (4,5), (4,3) |$

$=veci((5)*(-3)-(9)*(-3))-vecj((4)*(-3)-(9)*(4))+veck((4)*(3)-(4)*(5))$

$=〈12,-24,-8〉=vecc$

Verification by doing 2 dot products

$〈12,-24,-8〉.〈4,5,-9〉=(12)*(4)+(-24)*(5)+(-8)*(-9)=0$

$〈12,-24,-8〉.〈4,3,-3〉=(12)*(4)+(-24)*(3)+(-8)*(-3)=0$

So,

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

What is the cross product of <4 , 5 ,-9 ><4 , 5 ,-9 > and <4, 3 ,-3 ><4, 3 ,-3 >?