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Question: Answered & Verified by Expert
The perpendicular bisector of a line segment with end points 1,2,6 and -3,6,2 passes through -6,2,4 and has the equation of the form x+6l=y-2m=z-4n (Where l,m,n are integers, l is a prime number and l>0), then the value of lmn-l+m+n equals to
MathematicsThree Dimensional GeometryJEE Main
Options:
  • A -3
  • B -5
  • C -7
  • D -9
Solution:
2637 Upvotes Verified Answer
The correct answer is: -7
Midpoint of the line segment is 1-31,2+62,6+22-1,4,4
Parallel vector to the required line =-1+6i^+4-2j^+4-4k^
=5i^+2j^+0k^
Hence, equation of the line is
x+65-y-22=z-40
l=5, m=2, n=0

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