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Prove that |vecaxxvecb|^2 =det ((veca.ve...

Prove that `|vecaxxvecb|^2 =det ((veca.veca,veca.vecb),(veca.vecb,vecb.vecb))`

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Prove that (veca xx vecb)^2=|(veca.veca,veca.vecb),(veca.vecb,vecb.vecb)| .

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If veca and vecb are any two vectors , then prove that |vecaxxvecb|^(2)=|veca|^(2)|vecb|^(2)-(veca.vecb)^(2)=|{:(veca.veca,veca.vecb),(veca.vecb,vecb.vecb):}| or |vecaxxvecb|^(2)+(veca.vecb)^(2)=|veca|^(2)|vecb|^(2) (This is also known as Lagrange identily)