What is the cross product of $< 5, - 3, 1 >$ $<5, -3,1 >$ and $< - 5, 2, 3 >$ $<-5 ,2 ,3 >$ ?

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Answer 1 · 2016-12-21T06:30:23

The answer is $= ⟨ - 11, - 20, - 5 ⟩$ $=〈-11,-20,-5〉$

The cross product is obtained from the determinant

$| (hati,hatj,hatk), (d,e,f), (g,h,i) |$

where $〈d,e,f〉$ and $〈g,h,i〉$ are the 2 vectors.

Therefore,

$| (hati,hatj,hatk), (5,-3,1), (-5,2,3) |$

$=hati | (-3,1), (2,3) |-hatj | (5,1), (-5,3) |+hatk | (5,-3), (-5,2) |$

$=hati(-3*3-2*1)-hatj(5*3+5*1)+hatk(5*2-5*3)$

$=hati(-11)-hatj()20+hatk(-5)$

$=〈-11,-20,-5〉$

Verification , by doing a dot product

$〈-11,-20,-5〉.〈5,-3,1〉=(-55+60-5)=0$

$〈-11,-20,-5〉.〈-5,2,3〉=(55-40-15)=0$

What is the cross product of <5, -3,1 ><5,−3,1><5, -3,1 > and <-5 ,2 ,3 ><−5,2,3><-5 ,2 ,3 >?