What is the cross product of #[1, -2, -3]# and #[3, 7, 9]#?

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Answer 1 · 2018-03-24T13:20:44

The vector is #=〈3,-18,13〉#

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=〈1,-2,-3〉# and #vecb=〈3,7,9〉#

Therefore,

#| (veci,vecj,veck), (1,-2,-3), (3,7,9) | #

#=veci| (-2,-3), (7,9) | -vecj| (1,-3), (3,9) | +veck| (1,-2), (3,7) | #

#=veci((-2)*(9)-(-3)*(7))-vecj((1)*(9)-(-3)*(3))+veck((1)*(7)-(-2)*(3))#

#=〈3,-18,13〉=vecc#

Verification by doing 2 dot products

#〈3,-18,13〉.〈1,-2,-3〉=(3)*(1)+(-18)*(-2)+(13)*(-3)=0#

#〈3,-18,13〉.〈3,7,9〉=(3)*(3)+(-18)*(7)+(13)*(9)=0#

So,

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