for any three vectors, `veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca)` =

Explanation

To solve the problem \((\vec{a} - \vec{b}) \cdot ((\vec{b} - \vec{c}) \times (\vec{c} - \vec{a}))\), we can interpret this expression as a scalar triple product. Here’s a step-by-step solution:

### Step 1: Identify the vectors
Let:
- \(\vec{u} = \vec{a} - \vec{b}\)
- \(\vec{v} = \vec{b} - \vec{c}\)
- \(\vec{w} = \vec{c} - \vec{a}\)

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