What is the cross product of #<9,2,8 ># and #<6, -2, 7 >#?

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Answer 1 · 2018-03-06T13:40:58

The vector is #= <30,-15,-30>#

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=〈9,2,8〉# and #vecb=〈6,-2,7〉#

Therefore,

#| (veci,vecj,veck), (9,2,8), (6,-2,7) | #

#=veci| (2,8), (-2,7) | -vecj| (9,8), (6,7) | +veck| (9,2), (6,-2) | #

#=veci((2)*(7)-(8)*(-2))-vecj((9)*(7)-(8)*(6))+veck((9)*(-2)-(2)*(6))#

#=〈30,-15,-30〉=vecc#

Verification by doing 2 dot products

#〈30,-15,-30〉.〈9,2,8〉=(30)*(9)+(-15)*(2)+(-30)*(8)=0#

#〈30,-15,-30〉.〈6,-2,7〉=(30)*(6)+(-15)*(-2)+(-30)*(7)=0#

So,

#vecc# is perpendicular to #veca# and #vecb#