The locus of a point equidistant from two given points a and b is given by

Dear pallavi

locus of point will be perpendicular bisector of these two vector.

let the general point on the line is r

so line will pass through (a+b)/2

and r-(a+b)/2     and (b-a)  will be perpendicular

so {r-(a+b)/2 }.(b-a) =0

 r.(b-a) =1/2( |b|² -|a|²)

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