The value of the determinant \( \Delta = \left|\begin{matrix} 1 & a & bc \\ 1 & b & ca \\ 1 & c & ab \end{matrix}\right| \) where \( a, b, c \) are distinct real numbers, expanded along the first row \( R_1 \), simplifies to:

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Correct answer · Option A

\( (a-b)(b-c)(a-c) \)

Expanding gives \( 1(ab^2 - ac^2) - a(ab - c^2) + bc(c - b) = (a-b)(b-c)(c-a) \times (-1) = (a-b)(b-c)(a-c) \).