i. If `veca, vecb and vecc` are non-coplanar vectors, prove that vectors `3veca-7vecb-4vecc, 3veca-2vecb+vecc and veca+vecb+2vecc` are coplanar.

Explanation

To prove that the vectors \( \vec{u} = 3\vec{a} - 7\vec{b} - 4\vec{c} \), \( \vec{v} = 3\vec{a} - 2\vec{b} + \vec{c} \), and \( \vec{w} = \vec{a} + \vec{b} + 2\vec{c} \) are coplanar, we can use the scalar triple product. The vectors are coplanar if the scalar triple product \( \vec{u} \cdot (\vec{v} \times \vec{w}) = 0 \).

### Step 1: Write the vectors in terms of their coefficients
Let:
- \( \vec{u} = 3\vec{a} - 7\vec{b} - 4\vec{c} \)
- \( \vec{v} = 3\vec{a} - 2\vec{b} + \vec{c} \)
- \( \vec{w} = \vec{a} + \vec{b} + 2\vec{c} \)

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