Question

Question-

$What \: is \: the \: \: cross product \: of \:  (2i−3j+4k)  \: and (i+j−7k)?\ \textless \ br /\ \textgreater \ \ \textless \ br /\ \textgreater$
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Answer 1

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,-3,4〉# and #vecb=〈1,1,-7〉#

Therefore,

#| (veci,vecj,veck), (2,-3,4), (1,1,-7) | #

#=veci| (-3,4), (1,-7) | -vecj| (2,4), (1,-7) | +veck| (2,-3), (1,1) | #

#=veci((-3)*(-7)-(4)*(1))-vecj((2)*(-7)-(4)*(1))+veck((2)*(1)-(-3)*(1))#

#=〈17,18,5〉=vecc#

Verification by doing 2 dot products

#〈17,18,5〉.〈2,-3,4〉=(17)*(2)+(18)*(-3)+(5)*(4)=0#

#〈17,18,5〉.〈1,1,-7〉=(17)*(1)+(18)*(1)+(5)*(-7)=0#

So,

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