How to Calculate Angle Bisector of Two Planes?

Definition:

The bisector of an angle is the locus of points on the plane that are equidistant from the rays that form the angle.

Formula Used:

|A1X+B1Y+C1|/√A12+B12 =  ± |A2X+B2Y+C2|/√A22+B22 Where, A1,B1,C1,A2,B2,C2 = Coefficients X,Y                       = Coordinates

Example :

The coefficients values are as follows A1=3,B1=-4,C1=5,A2=6,B2=8,C2=1.Find the Angle bisector.

Given :

Coefficient values A1=3,B1=-4,C1=5,A2=6,B2=8,C2=1

To Find :

Angle bisector

Solution :

|3X-4Y+5|/√32+42=+|6X+8Y+1|/√62+82
(3X-4Y+5)/5 =(6X+8Y+1)/10
2(3X-4Y+5)=1(6X+8Y+1)
6x-8y+10 =6x+8y+1
=>-16y+9=0
|3X-4Y+5|/√32+42 =-|6X+8Y+1|/√62+82
(3X-4Y+5)/5 =(6X+8Y+1)/10
2(3X-4Y+5)=-1(6X+8Y+1)
6x-8y+10=-6x-8y-1
=>12x+11=0

Result :

Angle bisector is -16y+9=0, 12x+11=0

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