bisector of the two vector with a moving vector

Question

Hallo,

I'm asking the same question of some days ago but now i would like to add at the question one more step.

Below the code for the first step:

t = -20:0.1:20; 
plot3(zeros(size(t)),t,-t.^2); 
hold on i = 1; 
h = plot3([0 0],[0 t(i)],[0 -t(i)^2],'r'); 
for(i=2:length(t)) 
set(h,'xdata',[0 0],'ydata',[0 t(i)],'zdata',[0 -t(i)^2]); 
pause(0.01); 
end

Now I draw a second vector, fixed in the space, with the same origin of the moving vector, say [0 0 0] and the end at, e.g., [0 0 -200] (running the code is necessary to fix this point at [0 0 -200]). Of course, there is an angle between the two vector, having the same origin.

My questions: I would like to calculate the bisector of this angle and show how the bisector moves in the space, in connection to the motion of the first vector.

Could be possible to have the matlab code for this problem?

Thank's for the help

Vittorio