If `veca, vecb and vecc` are non-coplanar vectors, prove that the four points `2veca+3vecb-vecc, veca-2vecb+3vecc, 3veca+4vecb-2vecc and veca-6vecb+ 6 vecc` are coplanar.

Explanation

To prove that the four points \( P_1 = 2\vec{a} + 3\vec{b} - \vec{c} \), \( P_2 = \vec{a} - 2\vec{b} + 3\vec{c} \), \( P_3 = 3\vec{a} + 4\vec{b} - 2\vec{c} \), and \( P_4 = \vec{a} - 6\vec{b} + 6\vec{c} \) are coplanar, we will show that the vectors \( \vec{AB} \), \( \vec{AC} \), and \( \vec{AD} \) are coplanar.

### Step 1: Define the vectors
Let:
- \( \vec{O} \) be the origin.
- \( \vec{P_1} = 2\vec{a} + 3\vec{b} - \vec{c} \)
- \( \vec{P_2} = \vec{a} - 2\vec{b} + 3\vec{c} \)
- \( \vec{P_3} = 3\vec{a} + 4\vec{b} - 2\vec{c} \)
...