Show that points with position vectors `2veca-2vecb+3vecc,-2veca+3vecb-vecc` and `6veca-7vecb+7vecc` are collinear. It is given that vectors `veca,vecb` and `vecc` and non-coplanar.

Explanation

To show that the points with position vectors \( \vec{A} = 2\vec{a} - 2\vec{b} + 3\vec{c} \), \( \vec{B} = -2\vec{a} + 3\vec{b} - \vec{c} \), and \( \vec{C} = 6\vec{a} - 7\vec{b} + 7\vec{c} \) are collinear, we will follow these steps:

### Step 1: Find the vector \( \vec{AB} \)
The vector \( \vec{AB} \) can be found by subtracting the position vector of point A from the position vector of point B:

\[ \vec{AB} = \vec{B} - \vec{A} \]
...