Editing Bisection (section)

=== Perpendicular line segment bisectors in space ===
*The [[perpendicular]] bisector of a line segment is a ''plane'', which meets the segment at its [[midpoint]] perpendicularly. 
Its vector equation is literally the same as in the plane case:

'''(V)''' <math>\quad \vec x\cdot(\vec a-\vec b)=\tfrac 1 2 (\vec a^2-\vec b^2) .</math>

With <math>A=(a_1,a_2,a_3),B=(b_1,b_2,b_3)</math> one gets the equation in coordinate form:

'''(C3)''' <math>\quad (a_1-b_1)x+(a_2-b_2)y+(a_3-b_3)z=\tfrac 1 2 (a_1^2-b_1^2+a_2^2-b_2^2+a_3^2-b_3^2) \; .</math>

Property '''(D)''' (see above) is literally true in space, too:<br>
'''(D)''' The perpendicular bisector plane of a segment <math>AB</math> has for any point <math>X</math> the property: <math>\;|XA| = |XB|</math>.