What is the cross product of $[0, 8, 5]$ $[0,8,5]$ and $[1, 4, - 2]$ $[1, 4, -2]$ ?

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Answer 1 · 2017-04-03T15:05:58

The vector is $= ⟨ - 36, 5, - 8 ⟩$ $=〈-36,5,-8〉$

The cross product is a vector perpendiculat to 2 other vectors

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

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

Here, we have $veca=〈0,8,5〉$ and $vecb=〈1,4,-2〉$

Therefore,

$| (veci,vecj,veck), (0,8,5), (1,4,-2) |$

$=veci| (8,5), (4,-2) | -vecj| (0,5), (1,-2) | +veck| (0,8), (1,4) |$

$=veci(-2*8-5*4)-vecj(-2*0-5*1)+veck(0*4-8*1)$

$=〈-36,5,-8〉=vecc$

Verification by doing 2 dot products

$〈-36,5,-8〉.〈0,8,5〉=-36*0+5*8-5*8=0$

$〈-36,5,-8〉.〈1,4,-2〉=-36*1+5*4+2*8=0$

So,

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

What is the cross product of [0,8,5][0,8,5][0,8,5] and [1, 4, -2] [1,4,−2][1, 4, -2] ?