Show that the points with position vectors ` vec a-2 vec b+3 vec c ,\ -2 vec a+3 vec b- vec c\ a n d\ 4 vec a-7 vec b+7 vec c` are collinear.

Explanation

To show that the points with position vectors \( \vec{P} = \vec{a} - 2\vec{b} + 3\vec{c} \), \( \vec{Q} = -2\vec{a} + 3\vec{b} - \vec{c} \), and \( \vec{R} = 4\vec{a} - 7\vec{b} + 7\vec{c} \) are collinear, we can follow these steps:

### Step 1: Define the Position Vectors
Let:
- \( \vec{P} = \vec{a} - 2\vec{b} + 3\vec{c} \)
- \( \vec{Q} = -2\vec{a} + 3\vec{b} - \vec{c} \)
- \( \vec{R} = 4\vec{a} - 7\vec{b} + 7\vec{c} \)

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