Angle between two vectors is computed weirdly!

Hi all,

I am trying to compute the angle between line L1v and the verticle norm Nv via the dot product using the follwoing code. However, I can see that the resulting angle is comouted between the xaxis (the horizontal norm) rather than the verticle and I can't see why. If you can run the follwoing piece of code you can see wha tI mean.

close all;
clear all;

%boundary length 
L = 1; 
%number of points on S axis
ns = 25; 
%boundary variable
s = linspace(0,L,ns); 
%construct coordinates meshgrid
[X,Y] = meshgrid(s,s); 
% mesh needs X,Y and Z so create z
Z = zeros(size(X));
%Visualise the grid
figure;
mesh(X,Y,Z,'Marker','o','EdgeColor',"k") %or surf
axis equal tight
view(2)
set(gca,'ytick',[])
xlabel('$S$','Interpreter','latex')
set(gca,'TickLabelInterpreter','latex')
set(gca,'FontSize',16)
hold on
% %-----------------------------

%Compute first line equation | L1: Ax + By + C = 0 
%first line coordinates
x1L1 = 0.5;  y1L1 = 0;
x2L1 = 1  ;  y2L1 = 0.1;
%Setting the determinant to be zero to get the line's standrad formula
A = y1L1 - y2L1;
B = x2L1 - x1L1;
C = x1L1*y2L1 - x2L1*y1L1; %or C=-A*x1-B*y1
%L1 stamdard line equation
L1 = (-C/B)+(-A/B)*s; % -A/B is the gradient and -C/B is the intercept
%plotting on the grid
plot(s,L1,'b','LineWidth',2)
axis([min(s) max(s) min(s) max(s)])
%find the angle between L1 and the norm N
L1v = [x2L1,y2L1] - [x1L1,y1L1]; %compute the x and y projections of L1
%defining the vertical norm
%pos1 = randi(length(s));    vnorm = s(pos1);
vnorm = x1L1;
Nvx = [vnorm 0];  %the verticle normal vector 
%plot the verticle norm line
y=get(gca,'ylim');
hold on
plot([vnorm vnorm],y,'g','LineWidth',2)
%dot product between L1v and Nvx to get the angle
theta1 = acos((L1v(1,1) * Nvx(1,1)+L1v(1,2) * Nvx(1,2))/...
    (sqrt((L1v(1,1))^2+(L1v(1,2))^2)*sqrt((Nvx(1,1))^2+(Nvx(1,2))^2))); 
%show results on the screen
fprintf('The angle between the first line and the vertical norm: theta1=%g\n',...
    theta1*(180/pi)');

Any comments on that would be appreicted!

Thanks.

Answer 1

[Hrishikesh Borate]

Hi,

It’s my understanding that you are trying to find angle between line L1v and vertical normal Nv. This can be achieved by modifying the assignment of Nvx as follows :-

Nvx = [0 vnorm];  %the vertical normal vector 

[Lama Hamadeh]

Great! Thanks!