What is the cross product of #<-3,0, 2># and #<-1, -4, 1>#?

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Answer 1 · 2018-07-27T17:32:13

#<8,1,12>#

We make a 3x3 matrix, and find the determinant of it to find the cross product of the two vectors.

#((i,j,k),(-3,0,2),(-1,-4,1))#

The determinant of this matrix is:

#i*det((0,2),(-4,1)) - j*det((-3,2),(-1,1))+k*det((-3,0),(-1,-4))#

#i[(0)(1)-(2)(-4)]-j[(-3)(1)-(2)(-1)]+k[(-3)(-4)-(0)(-1)]#

#i(0+8)-j(-3+2)+k(12+0)#

#i(8)-j(-1)+k(12)#

#8i+j+12k#

In other words, the cross product of #<-3,0,2># and #<-1,-4,1># is the vector #<8,1,12>#.