If `veca xx vecb = vecb xx vecc ne 0 ` where `veca , vecb and vecc` are coplanar vectors, then for some scalar k prove that `veca+vecc = kvecb`.

Explanation

To prove that \(\vec{a} + \vec{c} = k \vec{b}\) for some scalar \(k\), given that \(\vec{a} \times \vec{b} = \vec{b} \times \vec{c} \neq 0\) and that \(\vec{a}, \vec{b}, \vec{c}\) are coplanar vectors, we can follow these steps:

### Step 1: Start with the given equation
We have:
\[ \vec{a} \times \vec{b} = \vec{b} \times \vec{c} \]

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