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JEE Main201815 Apr 2018Evening ShiftMathematicsThree Dimensional GeometryActual

A plane bisects the line segment joining the points (1,2,3) and (-3,4,5) at right angles. Then this plane also passes through the point.

Options

  1. A(-3,2,1)
  2. B(3,2,1)
  3. C(1,2,-3)
  4. D(-1,2,3)

Correct answer

A. (-3,2,1)

Step-by-step solution

Since the plane bisects the line joining the points (1,2,3) and (-3,4,5) then the plane passes through the midpoint of the line which is : aligned ( 1-3 2 , 2+4 2 , 5+3 2 ) ( -2 2 , .& . 6 2 , 8 2 ) & (-1,3,4) . aligned As plane cuts the line segment at right angle, so the direction cosines of the normal of the plane are (-3-1,4-2,5-3)=(-4,2,2) So the equation of the plane is : -4 x+2 y+2 z= As plane passes through (-1,3,4) so -4(-1)+2(3)+2(4)= =18 Therefore, equation of plane is : -4 x+2 y+2 z=18 Now, only (-3,2,1

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