What is the cross product of #[-2,0,3]# and #[1,-1,3] #?

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Answer 1 · 2016-11-20T15:36:12

The vector is #=〈3,9,2〉#

The cross product of 2 vectors is given by the determinant.

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

Where, #〈d,e,f〉# and #〈g,h,i〉# are the 2 vectors.

So, we have,

#| (hati,hatj,hatk), (-2,0,3), (1,-1,3) |#

#=hati | (0,3), (-1,3) |-hatj | (-2,3), (1,3) |+hatk | (-2,0), (1,-1) |#

#=hati(3)+hatj(9)+hatk(2)#

So the vector is #〈3,9,2〉#

To verify, we must do the dot products

#〈3,9,2〉.〈-2,0,3〉=-6+0+6=0#

#〈3,9,2〉.〈1,-1,3〉=3-9+6=0#