Plot a changing angle over time

Need help regarding the changing angle between 2 vectors of a moving object over time. The 2 vectors are namely the direction vector and the vector referencing to the origin. I am stuck here as i dont know how to proceed to plot the cos_theta over time. Also, i keep getting the dimension mismatch for my cos_theta. Kindly appreciate any help thanks!!

x_i=input('Enter the initial x location of the object: ');
y_i=input('Enter the initial y location of the object: ');
z_i=input('Enter the initial z location of the object: ');
x_f=input('Enter the final x location of the object: ');
y_f=input('Enter the final y location of the object: ');
z_f=input('Enter the final z location of the object: ');
Vel=input('Enter velocity of moving object: ');
N=input('points: ');

initial=[x_i;y_i;z_i];
final=[x_f;y_f;z_f];

direction=final-initial;                                 %Direction vector
coord=[linspace(x_i,x_f,N);linspace(y_i,y_f,N);linspace(z_i,z_f,N)];
dist=sqrt((x_f-x_i).^2+(y_f-y_i).^2+(z_f-z_i).^2);       %Distance between final and initial  pos
Total_time=dist./Vel;                                    %Total time required to travel
%STUCK FROM HERE ONWARDS

n=linspace(1,N,N);
t=linspace(0,Total_time,N);

cos_theta = dot(direction,coord(:,n))/(norm(direction)*norm(coord(:,n)));
plot(t, cos_theta);

[darova]

Is that we talking about?

[MarshMellow]

Something like this but im looking for the angle between the red line (direction vector between 2 points) and one of the vector pointing towards the origin.

Answer 1

[David Hill]

function angleOtime(initial,final,vel,n)
direction=final-initial;                              
dist=norm(direction);      
velocity=(direction/dist).*vel;
t=linspace(0,dist/vel,n);
cos_theta = arrayfun(@(x)dot(direction,x*velocity+initial)/(norm(direction)*norm(x*velocity+initial)),t);
plot(t, cos_theta);
end

If I understood you correctly, the above function should work for you. Just input the initial point [xi,yi,zi], final point [xf,yf,zf], vel, and number of interval desired.

[MarshMellow]

Thanks a lot! This is exactly what Im looking for! Im still a beginner at matlab and will study the function you provided!