What is the cross product of $<-2, 5 ,-2 >$ and $<7 , -9 ,2 >$ ?

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Answer 1 · 2017-01-29T11:10:12

The answer is $=<-8,-10,-17>$

The cross product of 2 vectors $veca$ and $vecb$ is given by the determinant

$|((hati ,hatj,hatk ), (-2,5,-2),(7,-9,2))|$

$=hati*|((5,-2),(-9,2))|-hatj*|((-2,-2),(7,2))|+hatk*|((-2,5),(7,-9))|$

$=hati(-8)-hatj(10)+hatk(-17)$

$=<-8,-10,-17>$

Verification by doing the dot products

$<-8,-10,-17>.<-2,5,-2>=16-50+34=0$

$<-8,-10,-17>.<7,-9,2>=-56+90-34=0$

What is the cross product of <-2, 5 ,-2 ><-2, 5 ,-2 > and <7 , -9 ,2 ><7 , -9 ,2 >?