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

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Answer 1 · 2018-07-27T17:32:13

$< 8, 1, 12 >$ $<8,1,12>$

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 $<8,1,12>$ .

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