If` veca , vec b , vec c` are the position vectors of the vertices `A ,B ,C` of a triangle `A B C ,` show that the area triangle `A B Ci s1/2| vec axx vec b+ vec bxx vec c+ vec cxx vec a|dot` Deduce the condition for points ` veca , vec b , vec c` to be collinear.

Explanation

To solve the problem step by step, we will find the area of triangle ABC using the position vectors of its vertices A, B, and C, and then deduce the condition for the points to be collinear.

### Step-by-Step Solution:

1. **Identify Position Vectors:**
Let the position vectors of points A, B, and C be represented as:
\[
\vec{a}, \vec{b}, \vec{c}
...