JEE Mains · Maths · STD 12 - 11. three dimension geometry
If the plane \(2 x + y -5 z =0\) is rotated about its line of intersection with the plane \(3 x-y+4 z-7=0\) by an angle of \(\frac{\pi}{2}\), then the plane after the rotation passes through the point
- A \((2,-2,0)\)
- B \((-2,2,0)\)
- C \((1,0,2)\)
- D \((-1,0,-2)\)
Answer & Solution
Correct Answer
(C) \((1,0,2)\)
Step-by-step Solution
Detailed explanation
\((2 x + y -5 z )+\lambda(3 x - y +4 z -7)=0\) Rotated by \(\pi / 2\) \((2+3 \lambda) x +(1-\lambda) y +(-5+4 \lambda) z -7 \lambda=0\) \(2 x + y -5 z =0\) \(2(2+3 \lambda)+(1-\lambda)-5(-5+4 \lambda)=0\) \(\Rightarrow 4+6 \lambda+1-\lambda+25-20 \lambda=0\) \(30=15 \lambda\)…
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