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📐 Mathematics  ·  Introduction to Three Dimensional Geometry  ·  JEE

The locus of a point equidistant from the points A and B in space is:

Answer: The plane perpendicular to AB through its midpoint.

  • A A sphere with AB as its diameter in most cases
  • B The single midpoint of AB and no other point
  • C The plane perpendicular to AB through its midpoint
  • D The straight line AB extended indefinitely

Correct answer: C. The plane perpendicular to AB through its midpoint

Explanation: Equating squared distances cancels the quadratic terms and leaves a linear equation - the perpendicular bisector plane of AB.

zxyOP(x, y, z)first octant:x>0, y>0, z>0

Concept context

Coordinate axes and planes in space, octants, distance between two points, and the section formula

Read the full Introduction to Three Dimensional Geometry notes →