What is the cross product of $[4, -4, 4]$ and $[-6, 5, 1]$ ?

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Answer 1 · 2018-07-19T16:05:06

$\begin{pmatrix}-24&-28&-4\end{pmatrix}$

Use the following cross product formula:

$(u1,u2,u3)xx(v1,v2,v3) = (u2v3 − u3v2 , u3v1 − u1v3 , u1v2 − u2v1)$

$(4,-4,4)xx(-6,5,1) = (-4*1 − 4*5 , 4*-6 − 4*1 , 4*5 − -4*-6)$

$=(-24,-28,-4)$

Answer 2 · 2018-07-19T16:19:29

The vector is $= 〈-24,-28,-4〉$

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 $veca=〈4,-4,4〉$ and $vecb=〈-6,5,1〉$

Therefore,

$| (veci,vecj,veck), (4,-4,4), (-6,5,1) |$

$=veci| (-4,4), (5,1) | -vecj| (4,4), (-6,1) | +veck| (4,-4), (-6,5) |$

$=veci((-4)*(1)-(5)*(4))-vecj((4)*(1)-(-6)*(4))+veck((4)*(5)-(-4)*(-6))$

$=〈-24,-28,-4〉=vecc$

Verification by doing 2 dot products

$〈4,-4,4〉.〈-24,-28,-4〉=(4)*(-24)+(-4)*(-28)+(4)*(-4)=0$

$〈-24,-28,-4〉.〈-6,5,1〉=(-24)*(-6)+(-28)*(5)+(-4)*(1)=0$

So,

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

What is the cross product of [4, -4, 4][4, -4, 4] and [-6, 5, 1] [-6, 5, 1] ?