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

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Answer 1 · 2016-11-13T20:41:38

The answer is $⟨ 3, 1, - 5 ⟩$ $〈3,1,-5〉$

Let $\to u = ⟨ 1, 2, 1 ⟩$ $vecu=〈1,2,1〉$

and $\to v = ⟨ 2, - 1, 1 ⟩$ $vecv=〈2,-1,1〉$

The cross product is given by the determinant

$∣ ((veci,vecj,veck) , (1,2,1) , (2,-1,1)) ∣$

$=veci(2+1)-vecj(1-2)+veck(-1-4)$

$=3veci+vecj-5veck$

$vecw=〈3,1,-5〉$

Verifications, by doing the dot product

$vecw.vecu=〈3,1,-5〉.〈1,2,1〉=3+2-5=0$

$vecw.vecv〈3,1,-5〉.〈2,-1,1〉=6-1-5=0$

So, $vecw$ is perpendicular to $vecu$ and $vecv$

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