\(\left| \begin{matrix} x^{ n } & { x }^{ n+2 } & { x }^{ n+3 } \\ { y }^{ n } & { y }^{ n+2 } & { y }^{ n+3 } \\ { z }^{ n } & { z }^{ n+2 } & { z }^{ n+3 } \end{matrix} \right| =(x-y)(y-z)(z-x)(\frac { 1 }{ x } +\frac { 1 }{ y } +\frac { 1 }{ z } )\), then \(n\) equals

Also see Coordinate Geometry

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