Cross Product

Why isn't the cross product associative?

Here is one reason.
$\displaystyle \begin{array}{l}
a \times \left( {b \times c} \right) = \left( {a \cdot c} \right)b - \left( {a \cdot b} \right)c \\
\left( {a \times b} \right) \times c = - c \times \left( {a \times b} \right) = \left( { - c \cdot b} \right)a - \left( { - c \cdot a} \right)b = (c \cdot a)b - \left( {c \cdot b} \right)a \\
\end{array}
$
Clearly these are not equal!

Quote:

---

Originally Posted by Plato

Here is one reason.
$\displaystyle \begin{array}{l}
a \times \left( {b \times c} \right) = \left( {a \cdot c} \right)b - \left( {a \cdot b} \right)c \\
\left( {a \times b} \right) \times c = - c \times \left( {a \times b} \right) = \left( { - c \cdot b} \right)a - \left( { - c \cdot a} \right)b = (c \cdot a)b - \left( {c \cdot b} \right)a \\
\end{array}
$
Clearly these are not equal!

---

Can you please explain how worked th first line: a cross (b cross c)

Quote:

---

Originally Posted by a.a

Can you please explain how worked th first line: a cross (b cross c)

---

Allow me to be brutally frank with you. If you are asking questions at this level then you are expected to know basic facts. You are expected to know basic rules and theorems. The function of sites such as this are not here to teach you the material but rather we want to help you understand the material by building upon the work that you have already done.

So you go look up in you textbook and answer that question for yourself.

I looked up the identities but for thiss proof we are supposed to prove useing components, how would we do this?