- #1
Saitama
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I am currently going through the book Introduction Of Electrodynamics by Griffiths. I have come across vector triple product which is stated as follows in the book:
$$\textbf{A} \times (\textbf{B} \times \textbf{C})=\textbf{B}(\textbf{A}\cdot \textbf{C})-\textbf{C}(\textbf{A}\cdot \textbf{B})$$
The author then states a few more vector products and says that they can be derived using the vector triple product. One of them I am unable to derive is :
$$(A\times B)\cdot (C\times D)=(A\cdot C)(B\cdot D)-(A\cdot D)(B\cdot C)$$
I don't see how I can derive the above using the vector triple product.![Confused :confused: :confused:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Any help is appreciated. Thanks!
$$\textbf{A} \times (\textbf{B} \times \textbf{C})=\textbf{B}(\textbf{A}\cdot \textbf{C})-\textbf{C}(\textbf{A}\cdot \textbf{B})$$
The author then states a few more vector products and says that they can be derived using the vector triple product. One of them I am unable to derive is :
$$(A\times B)\cdot (C\times D)=(A\cdot C)(B\cdot D)-(A\cdot D)(B\cdot C)$$
I don't see how I can derive the above using the vector triple product.
Any help is appreciated. Thanks!