Calculate angles correctly between two vectors using the dot product. (2024)

"However, and as shwon in the figure, it is clear that Theta2n = Theta1N + pi/2"

How exactly is that clear or shown?

"How can I caulcate these angles correctly using the dot product?"

Utilize these functions - dot, norm

% Close all figures and clear variables

close all;

clear all;

% Define the reference vector

L = [-0.5 -0.5];

% Define the first vector v1 and calculate the angle with L

v1 = [-0.6788 0.3214];

% Dot product of v1 and L

dot_v1_L = dot(v1, L);

% Norms of v1 and L

norm_v1 = norm(v1);

norm_L = norm(L);

% Angle theta1 with the x axis

theta1 = acos(dot_v1_L / (norm_v1 * norm_L));

% Angle theta1 with the norm

theta1norm = pi/2 - theta1;

% Define the second vector v2 and calculate the angle with L

v2 = [0.3214 -0.6788];

% Dot product of v2 and L

dot_v2_L = dot(v2, L);

% Norms of v2

norm_v2 = norm(v2);

% Angle theta2 with the x axis

theta2 = acos(dot_v2_L / (norm_v2 * norm_L));

% Angle theta2 with the norm

theta2norm = pi/2 - theta2;

% Convert angles to degrees

theta1_degree = radtodeg(theta1);

theta2_degree = radtodeg(theta2);

theta1norm_degree = radtodeg(theta1norm);

theta2norm_degree = radtodeg(theta2norm);

% Display the results

disp(['Theta1: ', num2str(theta1_degree), ' degrees']);

disp(['Theta2: ', num2str(theta2_degree), ' degrees']);

disp(['Theta1 from the norm: ', num2str(theta1norm_degree), ' degrees']);

disp(['Theta2 from the norm: ', num2str(theta2norm_degree), ' degrees']);

theta1 = cart2pol(L(1)/norm(L),L(2)/norm(L))*180/pi

if theta1 <=0

theta1 = 360 + theta1;

end

theta2 = cart2pol(v1(1)/norm(v1),v1(2)/norm(v1))*180/pi

if theta2 <=0

theta2 = 360 + theta2;

end

theta3 = cart2pol(v2(1)/norm(v2),v2(2)/norm(v2))*180/pi

if theta3 <=0

theta3 = 360 + theta3;

end