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📰 #### 8Question: Given three vertices of a cube at \((1, 2, 3)\), \((1, 5, 3)\), and \((4, 2, 3)\), find the coordinates of the fourth vertex that is diagonally opposite to \((1, 2, 3)\) on the same face, assuming all coordinates are integers.
📰 Solution: The given points lie on the plane \(z = 3\). The vector from \((1, 2, 3)\) to \((1, 5, 3)\) is \((0, 3, 0)\), and the vector to \((4, 2, 3)\) is \((3, 0, 0)\). The fourth vertex on the same face is obtained by adding these vectors: \((1 + 3, 2 + 3, 3) = (4, 5, 3)\).
📰 \boxed{(4, 5, 3)}
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