AP EAMCET · Maths · Three Dimensional Geometry
The equation of the plane mid-parallel to the planes \(2 x-3 y+6 z+21=0\) and \(2 x-3 y+6 z-14=0\) is given by
- A \(4 x+6 y-12 z+7=0\)
- B \(4 x-6 y-12 z-7=0\)
- C \(4 x-6 y+12 z+7=0\)
- D \(4 x+6 y+12 z-7=0\)
Answer & Solution
Correct Answer
(C) \(4 x-6 y+12 z+7=0\)
Step-by-step Solution
Detailed explanation
Let equation of plane \(2 x-3 y+6 z+d=0\) is equidistance from two parallel planes \[ 2 x-3 y+6 z+21=0 \text { and } 2 x-3 y+6 z-14=0 \] So, \(\frac{|21-d|}{\sqrt{4+9+36}}=\frac{|d+14|}{\sqrt{4+9+36}} \Rightarrow 21-d=d+14\)…
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