The planes $\lambda x+y+z=\lambda-1,x+\lambda y+z=\lambda-1,x+y+\lambda z=\lambda-1$ form a triangular prism.

Question

The planes $\lambda x+y+z=\lambda-1,x+\lambda y+z=\lambda-1,x+y+\lambda z=\lambda-1$ form a triangular prism.Then find the value of $\lambda $.And find the distance of the origin from an edge of the prism.

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Is there a method or formula by which $\lambda $ can be found out.Please help me.