What is the cross product of $< 3, 1, - 6 >$ $<3 ,1 ,-6 >$ and $< - 2, 1, 8 >$ $<-2 ,1 , 8 >$ ?

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Answer 1 · 2018-04-20T16:22:55

$< 14, - 12, 5 >$ $<14,-12,5>$

we want

$< 3, 1, - 6 > \times < - 2, 1, 8 >$ $<3,1,-6>xx<-2,1,8>$

this is found by calculating the determinant

$|(hati,hatj,hatk),(3,1,-6),(-2,1,8)|$

expand by row 1

$hati|(1,-6),(1,8)|-hatj|(3,-6),(-2,8)|+hatk|(3,1),(-2,1)|$

$=hati(8 --6)-hatj(24- 12)+hatk(3- -2)$

$14hati-12hatj+5hatk$

$= <14,-12,5>$

What is the cross product of <3 ,1 ,-6 ><3,1,−6><3 ,1 ,-6 > and <-2 ,1 , 8 ><−2,1,8><-2 ,1 , 8 >?