show that `(vecaxxvecb)xxvecc=vecaxx(vecbxxvecc)` if and only if `veca and vecc` are collinear or `(vecaxxvecc)xxvecb=vec0`

Explanation

To show that \((\vec{a} \times \vec{b}) \times \vec{c} = \vec{a} \times (\vec{b} \times \vec{c})\) if and only if \(\vec{a}\) and \(\vec{c}\) are collinear or \((\vec{a} \times \vec{c}) \times \vec{b} = \vec{0}\), we will follow these steps:

### Step 1: Use the Vector Triple Product Identity
Recall the vector triple product identity, which states:
\[ \vec{x} \times (\vec{y} \times \vec{z}) = (\vec{x} \cdot \vec{z}) \vec{y} - (\vec{x} \cdot \vec{y}) \vec{z} \]
We will apply this identity to both sides of the equation we need to prove.
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