What is the cross product of $[- 2, 0, 3]$ $[-2,0,3]$ and $[1, - 1, 3]$ $[1,-1,3]$ ?

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Answer 1 · 2016-11-20T15:36:12

The vector is $= ⟨ 3, 9, 2 ⟩$ $=〈3,9,2〉$

The cross product of 2 vectors is given by the determinant.

$| (hati,hatj,hatk), (d,e,f), (g,h,i) |$

Where, $〈d,e,f〉$ and $〈g,h,i〉$ are the 2 vectors.

So, we have,

$| (hati,hatj,hatk), (-2,0,3), (1,-1,3) |$

$=hati | (0,3), (-1,3) |-hatj | (-2,3), (1,3) |+hatk | (-2,0), (1,-1) |$

$=hati(3)+hatj(9)+hatk(2)$

So the vector is $〈3,9,2〉$

To verify, we must do the dot products

$〈3,9,2〉.〈-2,0,3〉=-6+0+6=0$

$〈3,9,2〉.〈1,-1,3〉=3-9+6=0$

What is the cross product of [-2,0,3][−2,0,3][-2,0,3] and [1,-1,3] [1,−1,3][1,-1,3] ?