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, we will follow these steps:

### Step 1: Define the position vectors
Let the position vectors of the vertices \( A, B, C \) of triangle \( ABC \) be denoted by \( \vec{a}, \vec{b}, \vec{c} \).

### Step 2: Find the vectors \( \vec{AB} \) and \( \vec{AC} \)
The vector \( \vec{AB} \) can be expressed as:
\[
...