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

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

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

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