What is the cross product of #[3, 1, -4]# and #[2, 6, -1] #?

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Answer 1 · 2016-08-24T08:57:39

#= 23 hat x -5 hat y + 16 hat z#

the cross product you seek is the determinant of the following matrix

#((hat x, hat y , hat z),(3,1,-4),(2,6,-1))#

#= hat x(1*(-1) - (-4)*6) - hat y (3 \* (-1) - (-4)*2) + hat z (3*6 - 2*1)#

#= 23 hat x -5 hat y + 16 hat z#

this should be perpendicular to these 2 vectors and we can check that via the scalar dot product

#<23 , -5 , 16 >* <3,1,-4> = 69 - 5 - 64 = 0#

#<23 , -5 , 16 >* <2,6,-1> = 46 - 30 -16 = 0#