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Question: Answered & Verified by Expert
If $l, m, n$ are the d.c's of a normal to the plane passing through the points $(0,1,2),(3,0,2),(4,5,0)$ then $|l|+|m|+|n|=$
MathematicsThree Dimensional GeometryTS EAMCETTS EAMCET 2022 (20 Jul Shift 2)
Options:
  • A $\frac{13}{\sqrt{91}}$
  • B $\frac{11}{\sqrt{57}}$
  • C $\frac{13}{\sqrt{77}}$
  • D $\frac{12}{\sqrt{74}}$
Solution:
1977 Upvotes Verified Answer
The correct answer is: $\frac{12}{\sqrt{74}}$
The plane passing through points $(0,1,2)(3,0,2)$, $(4,5,0)$ can be given as $2 x+6 y+16 z-38=0$
Now $|1|+|\mathrm{m}|+|\mathrm{n}|=\frac{12}{\sqrt{74}}$

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