Consider the following three planes:P : x + y | vedclass

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(C) The normal vectors to the planes are:$\vec{n}_P = (1, 1, -2)$$\vec{n}_Q = (1, 1, 2)$$\vec{n}_R = (3, 3, -6)$Two planes are parallel if their norma

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$P$ and $R$ are parallel.

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(C) The normal vectors to the planes are:$\vec{n}_P = (1, 1, -2)$$\vec{n}_Q = (1, 1, 2)$$\vec{n}_R = (3, 3, -6)$Two planes are parallel if their normal vectors are proportional. For $P$ and $R$,we check the ratio of components:$\frac{1}{3} = \frac{1}{3} = \frac{-2}{-6} = \frac{1}{3}$.Since the normal vectors $\vec{n}_P$ and $\vec{n}_R$ are proportional,the planes $P$ and $R$ are parallel.Therefore,the correct option is $C$.

Consider the following three planes:
$P : x + y - 2z + 7 = 0$
$Q : x + y + 2z + 2 = 0$
$R : 3x + 3y - 6z - 11 = 0$

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Consider the following three planes:$P : x + y - 2z + 7 = 0$$Q : x + y + 2z + 2 = 0$$R : 3x + 3y - 6z - 11 = 0$