Using vectors, find the area of the triangle with vertices `A(1,1,2),\ B(2,3,5)a n d\ C(1,5,5)`

Explanation

To find the area of the triangle with vertices \( A(1,1,2) \), \( B(2,3,5) \), and \( C(1,5,5) \) using vectors, we can follow these steps:

### Step 1: Determine the position vectors of points A, B, and C.
The position vectors can be represented as:
\[ \vec{A} = \begin{pmatrix} 1 \\ 1 \\ 2 \end{pmatrix}, \quad \vec{B} = \begin{pmatrix} 2 \\ 3 \\ 5 \end{pmatrix}, \quad \vec{C} = \begin{pmatrix} 1 \\ 5 \\ 5 \end{pmatrix} \]

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