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Let the plane ax +by+cz+d=0 bisect the l...

Let the plane `ax +by+cz+d=0` bisect the line joining the points (4, -3,1) and (2, 3, -5) at the right angles। If a, b, c, d are integers, then the minimum value of `(a^2 + b^2 + c^2 + d^2)` is_______.

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The plane which bisects the line joining the points (4, -2, 3) and (2,4,-1) at right angles also passes through the point :

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Knowledge Check

  • The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles, is

    A
    `x+y+z=0`
    B
    `x+y-z=0`
    C
    `x+y+z=9`
    D
    `x+y-z+9=0`
  • The intercepts made on the axes by the plane which bisects the line joining the points (1, 2, 3) and (-3,4,5) at right angle, are

    A
    `(-9/2,9,9)`
    B
    `(9/2,-9,9)`
    C
    `(19,-9/2,9)`
    D
    `(9,9/2,19)`
  • Equation of the plane which bisects the join of the points A(3,-1,4) and B(-3,5,2) at right angles is

    A
    3x-3y+z+3=0
    B
    3x-3y-z+3=0
    C
    3x+3y+z=3
    D
    3x+3y-z=3
  • Similar Questions

    Explore conceptually related problems

    Find the equation of the plane that bisects the line segment joining points (1, 2, 3) and (3, 4, 5) and is at right angle to it.

    Write the cartesian equation of a plane, bisecting the line segment joining the points A (2,3,5) and B(4,5,7) at right angles.

    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:

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    The intercepts made on the x, y and z axes, by the plane which bisects the line joining the points (1,2,3) and (-3, 4,5) at right angles, are a,b and c respectively, then the ordered triplet (a,b,c) is