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

Question

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

Accepted Answer

Normals of $P$ and $R$: $(1,1,-2)$ and $(3,3,-6)=3(1,1,-2)$ --- proportional, so $P\parallel R$.

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