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

Question

1736 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-05T12:59:04

The vector is $=〈57,-6,-18〉$

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 $veca=〈2,4,5〉$ and $vecb=〈2,-5,8〉$

Therefore,

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

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

$=veci((4)*(8)-(5)*(-5))-vecj((1)*(3)-(1)*(1))+veck((-1)*(1)-(2)*(1))$

$=〈57,-6,-18〉=vecc$

Verification by doing 2 dot products

$〈57,-6,-18〉.〈2,4,5〉=(57)*(2)+(-6)*(4)+(-18)*(5)=0$

$〈57,-6,-18〉.〈2,-5,8〉=(57)*(2)+(-6)*(-5)+(-18)*(8)=0$

So,

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

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