The determinant \( \left|\begin{array}{ccc}x p+y & x & y \\ y p+z & y & z \\ 0 & x p+y & y p+z\e...

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The determinant \( \left|\begin{array}{ccc}x p+y & x & y \\ y p+z & y & z \\ 0 & x p+y & y p+z\end{array}\right|=0 \) for all \( p \in R \) if
(a) \( x, y, z \) are in AP
(b) \( x, y, z \) are in GP
(c) \( x, y, z \) are in HP
(d) \( x y, y z, z x \) are in AP
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