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Where $A$ and $B$ are vectors, and $\times$ is the cross product operator. I was able to get $A(A \cdot B) - B$ using the vector triple product, but it doesn't look like a simplified version to me.

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    I'm sorry, I meant x is the cross product.2012-02-14

1 Answers 1

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Firstly note that, the vector triple product you want to evaluate is actually: $A \times (A \times B)=(A\cdot B)A-(|A|^2)B$

And this is, in fact, the most simplified expression that we can arrive at with what little you have given us!

Try to prove a more general following result:

$A \times (B \times C)=(A \cdot C)B-(A \cdot B)C$

Hint: Take, $A=a_1\hat i+a_2 \hat j+a_3 \hat k$ and so on for other vectors and do brute force computation.