math - Bisector of two vectors in 2D (may be collinear) -


how find bisecor b = (bx, by) of 2 vectors in general (we consider 2 non–zero vectors u = (ux, uy), v = (vx, vy), may collinear ).

for non-collinear vector can write: 

bx = ux/|u| + vx / |v| = uy/|u| + vy / |v|

but collinear vectors 

bx = = 0.

example:

u = (0 , 1) v = (0, -1) b = (0, 0)

to find unit bisection vectors of u , v.

if u/|u|+v/|v| !=0  first calculate unit vector of u , v  use parallelogram rule bisection (just add them)  since both have unit of 1, sum bisector vector   calculate unit vector of calculated vector.  else (if u/|u|+v/|v| ==0):  (if use method above, it's indintermination: 0*infinity=?)   if want bisector of (u0v) if u/|u| = (cos(t),sin(t))   take b=(cost(t+pi/2),sin(t+pi/2)) = (-sin(t),cos(t) )as bisector  therefore if u/|u|=(a1,a2) chose b=(-a2,a1)

example:

u=(0,1) v=(0,-1) bisector of (u0v): b=(-1,0)

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