Just like we have it in 2D coordinate geometry, is there an equation which describes the angle bisector of two straight lines in 3D coordinate geometry?

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Eynardfb0 · Accepted Answer

Let direction vectors of lines be                     l        1            →       and                     l        2            →      . And let the position vector of point of intersection of these lines be             p      →      .Note that if we add and subtract equi-modular vectors which are in direction of                     l        1            →       and                     l        2            →      , we will obtain direction vectors of angular bisectors (You can show this by   R  H  S congruency of triangles). Here I consideblack unimodular vectors                     l        1            ^       and                     l        2            ^      The direction vectors of angular bisectors can be written as                     b        1            →        =                    l        1            ^        +                    l        2            ^       and                     b        2            →        =                    l        1            ^        −                    l        2            ^      So the angular bisector lines will be            r      →        =            p      →        +  k                    b        1            →                    r      →        =            p      →        +  k                    b        2            →

Just like we have it in 2D coordinate geometry, is there an equation which describes the angle bisector of two straight lines in 3D coordinate geometry?

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