The three planes $4 y + 6 z = 5, 2 x + 3 y + 5 z = 5, 6 x + 5 y + 9 z = 10$

meet in a point

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have a line in common

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form a triangular prism

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meet at infinite number of points

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Solution

The correct option is D have a line in common
Given three planes are 4 $y + 6 z = 5, 2 x + 3 y + 5 z = 5, 6 x + 5 y + 9 z = 10$
Determinant of coefficient of the given planes is,
$= ∣ ∣ ∣ ∣ \begin{matrix} 0 & 4 & 6 2 & 3 & 5 6 & 5 & 9 \end{matrix} ∣ ∣ ∣ ∣ = - 4 (18 - 30) + 6 (10 - 18) = 0$
Therefore, given planes have a line in common.

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