What is the cross product of #[5, 6, -3]# and #[5, 2, 9]#?

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Answer 1 · 2017-01-29T10:58:16

The answer is #<60,-60,-20>#

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

#|((hati ,hatj,hatk ), (5,6,-3),(5,2,9))|#

#=hati*|((6,-3),(2,9))|-hatj*|((5,-3),(5,9))|+hatk*|((5,6),(5,2))|#

#=hati(60)-hatj(60)+hatk(-20)#

#=<60,-60,-20>#

Verification by doing the dot products

#<60,-60,-20>.<5,6,-3>=300-360+60=0#

#<60,-60,-20>.<5,2,9>=300-120-180=0#