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

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

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Answer 1 · 2017-03-04T09:39:10

$[16, 4, - 13] .$ $[16,4,-13].$

Explanation:

$[2,5,4]xx[1,-4,0]=|(i,j,k),(2,5,4),(1,-4,0)|,$

$=16i+4j-13k,$

$=[16,4,-13].$

Answer 2 · 2017-03-04T09:44:02

The vector is $=〈16,4,-13〉$

Explanation:

The vector perpendicular to 2 vectors is calculated with the determinant (cross product)

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

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

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

Therefore,

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

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

$=veci(16)-vecj(-4)+veck(-13)$

$=〈16,4,-13〉=vecc$

Verification by doing 2 dot products

$veca.vecc$

$=〈2,5,4>.〈16,4,-13〉=32+20-52=0$

$vecb.vecc$

$=〈1,-4,0〉.〈16,4,-13〉=16-16+0=0$

So,

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

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

2 Answers

Explanation:

Explanation:

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