COMEDK · Maths · 34. Three Dimensional Geometry
The equation of a plane passing through the line of intersection of the planes \(x+2 y+3 z=2\), \(x-y+z=3\) and at a distance \(\dfrac{2}{\sqrt{3}}\) from the point \((3,1,-1)\) is
- A \(5 x-11 y+z=17\)
- B \(\sqrt{2} x+y=3 \sqrt{2}-1\)
- C \(x+y+z=\sqrt{3}\)
- D \(x-\sqrt{2} y=1-\sqrt{2}\)
Answer & Solution
Correct Answer
(A) \(5 x-11 y+z=17\)
Step-by-step Solution
Detailed explanation
The equation of a plane passing through the intersection of the planes \(P_1: x + 2y + 3z - 2 = 0\) and \(P_2: x - y + z - 3 = 0\) is given by \(P_1 + \lambda P_2 = 0\). \((x + 2y + 3z - 2) + \lambda(x - y + z - 3) = 0\)…
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