Consider the following planes: P: x + y - 2z | vedclass

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(D) The given planes are:$P: x + y - 2z + 7 = 0$$Q: x + y + 2z + 2 = 0$$R: 3x + 3y - 6z - 11 = 0$To check if planes are parallel,we compare the ratios

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$P$ and $R$ are parallel

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(D) The given planes are:$P: x + y - 2z + 7 = 0$$Q: x + y + 2z + 2 = 0$$R: 3x + 3y - 6z - 11 = 0$To check if planes are parallel,we compare the ratios of the coefficients of $x, y,$ and $z$.For plane $P$,the normal vector is $\vec{n_1} = (1, 1, -2)$.For plane $R$,the normal vector is $\vec{n_2} = (3, 3, -6)$.We observe that $\vec{n_2} = 3(1, 1, -2) = 3\vec{n_1}$.Since the normal vectors are proportional,the planes $P$ and $R$ are parallel.Thus,the correct option is $D$.

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

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