Find the value of p if the points A(2,-1,1),B(4,0,p),C(1,1,1) and D(2,4,3) are coplanar.

Explanation

To determine the value of \( p \) for which the points \( A(2,-1,1) \), \( B(4,0,p) \), \( C(1,1,1) \), and \( D(2,4,3) \) are coplanar, we can use the concept of vectors and the scalar triple product. The points are coplanar if the volume of the parallelepiped formed by the vectors \( \overrightarrow{AB} \), \( \overrightarrow{AC} \), and \( \overrightarrow{AD} \) is zero.

### Step 1: Find the vectors \( \overrightarrow{AB} \), \( \overrightarrow{AC} \), and \( \overrightarrow{AD} \).

1. **Calculate \( \overrightarrow{AB} \)**:
\[ \overrightarrow{AB} = B - A = (4 - 2, 0 - (-1), p - 1) = (2, 1, p - 1) \]
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