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AP EAMCET202018 Sep 2020Morning ShiftMathematicsVector AlgebraActual

Equation of the perpendicular bisector of the line joining the points whose position vectors are ( a ) and ( b ) respectively is

Options

  1. A((2 r - a - b ) ( a - b )=0 )
  2. B((2 r - a - b ) ( a + b )=0 )
  3. C((2 r + a + b ) ( a - b )=0 )
  4. D((2 r - a + b ) ( a + b )=0 )

Correct answer

A. ((2 r - a - b ) ( a - b )=0 )

Step-by-step solution

The mid-point of line joining points whose position vectors are ( a ) and ( b ) is (M ( a + b 2 ) ) and the direction ratio vector of line joining of given points is (( a - b ) ). Let a variable point (p( r ) ) on the perpendicular bisector of (A B ), so ( M P B A ) ( array ll & ( r - a + b 2 ) ( a - b )=0 & (2 r - a - b ) ( a - b )=0 array )

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