if $A,B, C$ are non coplanar vectors and $(A\times B)\times C=A\times(B\times C)=0$ then A and B are perpendicular, B and C are perpendicular The vectors $A\neq 0$, $B\neq 0$ and $C\neq 0$. I don't understand how to used the fact that aren't coplanars. Do you know how to used it?

I've work in $(A\times B)\times C=A\times(B\times C)$ so
\begin{equation}
C=\frac{B\cdot C}{A\cdot B}A
\end{equation}
where $\cdot$ is the dot product, in this part, I know that $A$ and $C$ are parallel but I don't need to show that.
 A: 
I know that $A$ and $C$ are parallel

No, the question has clearly stated that $A$ and $C$ are not coplanar and hence they are not parallel.
Using the vector triple product formula, we may rewrite the condition $(A\times B)\times C=A\times (B\times C)=0$ as $(C\cdot A)B-(C\cdot B)A=(A\cdot C)B-(A\cdot B)C=0$. That is, $(B\cdot C)A=(A\cdot C)B=(A\cdot B)C$. Since $A,B$ and $C$ are non-coplanar nonzero vectors, we must have $B\cdot C=A\cdot C=A\cdot B=0$. Therefore $A,B$ and $C$ are perpendicular to each other.
A: You may weaken the assumption. Assume that $A$, $B$ and $C$ are all non-zero vectors and that they are not co-linear. Then the conditions $A\times(B\times C)=0$ and $(A\times B) \times C=0$ imply that the three vectors are mutually orthogonal.
You may use the formula for the triple vector product to arrive at the conclusion (as done elsewhere) but here is a more geometric argument:
We note that for two vectors $U$ and $V$, the cross product $U\times V$ is orthogonal to $U$ and to $V$. Also $U\times V=0$ iff $U\parallel  V$. (we allow for zero vectors).

*

*The condition $A\times(B\times C)=0$ implies that $A \parallel(B\times C)$ so either $B\parallel C$ or we have that $A$ is orthogonal to $B$ and to $C$.


*$(A\times B)\times C=0$ implies that $C\parallel (A\times B)$ so either $A\parallel B$ or we have that $C$ is orthogonal to $A$ and to $B$.
If $B\parallel C$ then $B$ can not be orthogonal to $C$ (since both are assumed non-zero) so by 2. we must have $A\parallel B$ as well. But then the three vectors are all co-linear which was excluded.
So we must have that $A$ is orthogonal to $B$ and to $C$, and that $C$ is orthogonal to $A$ and to $B$, i.e. the three vectors are mutually orthogonal.
