Prove that four points `2 vec a+3 vec b- vec c , vec a-2 vec b+3 vec c ,3 vec a+4 vec b-2 vec ca n d vec a-6 vec b+6 vec c` are coplanar.

Explanation

To prove that the four points \( P = 2\vec{a} + 3\vec{b} - \vec{c} \), \( Q = \vec{a} - 2\vec{b} + 3\vec{c} \), \( R = 3\vec{a} + 4\vec{b} - 2\vec{c} \), and \( S = \vec{a} - 6\vec{b} + 6\vec{c} \) are coplanar, we can use the concept of vectors and linear combinations.

### Step 1: Define the vectors
Let:
- \( \vec{P} = 2\vec{a} + 3\vec{b} - \vec{c} \)
- \( \vec{Q} = \vec{a} - 2\vec{b} + 3\vec{c} \)
- \( \vec{R} = 3\vec{a} + 4\vec{b} - 2\vec{c} \)
- \( \vec{S} = \vec{a} - 6\vec{b} + 6\vec{c} \)
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