If `vecb` and `vecc` are unit vectors, then for any arbitary vector `veca, (((veca xx vecb) + (veca xx vecc))xx (vecb xx vecc)) .(vecb -vecc)` is always equal to

Explanation

To solve the problem, we need to evaluate the expression:

\[ (((\vec{a} \times \vec{b}) + (\vec{a} \times \vec{c})) \times (\vec{b} \times \vec{c})) \cdot (\vec{b} - \vec{c}) \]

where \(\vec{b}\) and \(\vec{c}\) are unit vectors.

### Step 1: Expand the Cross Product
We start by expanding the expression inside the first cross product:

\[ \vec{a} \times \vec{b} + \vec{a} \times \vec{c} \]

This gives us two vectors that we will cross with \(\vec{b} \times \vec{c}\).