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

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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#