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

P and R are perpendicular
Q and R are perpendicular
P and Q are parallel
P and R are parallel

Correct answer: P and R are parallel

Solution

Planes P and R are parallel because their normal vectors, derived from the coefficients of x, y, and z in their equations, are scalar multiples of each other, indicating that they do not intersect.

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