Cross Product : Prove that | a × b | = . . .
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pka
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Re: Cross Product : Prove that | a × b | = . . .
Use the two identities .
\(\displaystyle \begin{array}{l}\left( {A \times B} \right)\cdot \left({C\times D} \right)=\left( {A \cdot C}\right)\left({B \cdot D}\right)-\left({A \cdot D}\right)\left({B \cdot C} \right)\\\left\|{A\times B}\right\|^2=\left( {A\times B} \right)\cdot\left( {A\times B}\right)\\\end{array}\)
Use the two identities .
\(\displaystyle \begin{array}{l}\left( {A \times B} \right)\cdot \left({C\times D} \right)=\left( {A \cdot C}\right)\left({B \cdot D}\right)-\left({A \cdot D}\right)\left({B \cdot C} \right)\\\left\|{A\times B}\right\|^2=\left( {A\times B} \right)\cdot\left( {A\times B}\right)\\\end{array}\)