What is the cross product of $[2, 1, -4]$ and $[3, 2, 5]$ ?

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Answer 1 · 2015-12-19T17:56:54

$(13,-22,1)$

By definition, the vector cross product of these two 3-dimensional vectors in $RR^3$ may be given by the following matrix determinant :

$(2,1,-4)xx(3,2,5)=|(hati,hatj,hatk),(2,1,-4),(3,2,5)|$

$=hati(5+8)-hatj(10+12)+hatk(4-3)$

$=13hati-22hatj+hatk$

$=(13,-22,1)$

What is the cross product of [2, 1, -4][2, 1, -4] and [3, 2, 5] [3, 2, 5] ?