Consider three planes $P_{1} : x - y + z = 1$ , $P_{2} : x + y - z = - 1$ and $P_{3} : x - 3 y + 3 z = 2$ Let $L_{1}, L_{2}$ and $L_{3}$ be the lines of intersection of the planes $P_{2} and P_{3}$ , $P_{3} and P_{1}$ and $P_{1} and P_{2}$ respectively.Statement 1: At least two of the lines $L_{1}, L_{2} and L_{3}$ are non-parallel The three planes do not have a common point

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Consider three planes

P_{1} : x - y + z = 1

P_{2} : x + y - z = - 1

and

P_{3} : x - 3 y + 3 z = 2

Let

L_{1}, L_{2}

and

L_{3}

be the lines of intersection of the planes

P_{2} and P_{3}

P_{3} and P_{1}

and

P_{1} and P_{2}

respectively.Statement 1: At least two of the lines

L_{1}, L_{2} and L_{3}

are non-parallel The three planes do not have a common point

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Question Text

Consider three planes

P_{1} : x - y + z = 1

P_{2} : x + y - z = - 1

and

P_{3} : x - 3 y + 3 z = 2

Let

L_{1}, L_{2}

and

L_{3}

be the lines of intersection of the planes

P_{2} and P_{3}

P_{3} and P_{1}

and

P_{1} and P_{2}

respectively.Statement 1: At least two of the lines

L_{1}, L_{2} and L_{3}

are non-parallel The three planes do not have a common point

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