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

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Answer 1 · 2017-01-06T06:16:27

The answer is $= ⟨ - 6, - 1, - 4 ⟩$ $=〈-6,-1,-4〉$

The cross product of 2 vectors, $⟨ a, b, c ⟩$ $〈a,b,c〉$ and $d, e, f ⟩$ $d,e,f〉$

is given by the determinant

$| (hati,hatj,hatk), (a,b,c), (d,e,f) |$

and $| (a,b), (c,d) |=ad-bc$

Here, the 2 vectors are $〈1,-2,-1〉$ and $〈-2,0,3〉$

And the cross product is

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

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

$=hati(-6+0)-hati(3-2)+hatk(0-4)$

$=〈-6,-1,-4〉$

Verification, by doing the dot product

$〈-6,-1,-4〉.〈1,-2,-1〉=-6+2+4=0$

$〈-6,-1,-4〉.〈-2,0,3〉=12+0-12=0$

Therefore, the vector is perpendicular to the other 2 vectors

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