How to generate a random 3D vector with set magnitude?

Hello, I am currently trying to figure out how to generate a random vector that differs in x,y,z values however thewir total magnitude is always set within a certain precision, so they can vary a bit in magnitude but would want them as close to the one aimed for.

I am currently looking at random generation and thinking about different ways but having trouble thinking how I would implement it in better way than just keep generating the random values until they are close enough.

Any help or guidance is appreciated.

Thank you for yoru time.

[Dyuman Joshi]

This might be helpful - https://in.mathworks.com/matlabcentral/answers/1745990-how-to-get-a-data-set-using-mean-and-standard-deviation?s_tid=srchtitle

Answer 1

[Hassaan]

targetMagnitude = 10; % Target magnitude of the vector
tolerance = 0.1; % Tolerance for the magnitude
nVectors = 5; % Number of vectors to generate

randomVectors = generateRandomVector(targetMagnitude, tolerance, nVectors);
disp(randomVectors);

   -3.9578    8.8378    2.4159
    5.5197   -6.9073    4.5746
   -0.5939   10.0319   -0.4312
    9.8464    1.1230   -1.4840
   -4.8208    7.0865    5.0712

function vectors = generateRandomVector(targetMag, tolerance, nVectors)
    vectors = zeros(nVectors, 3); % Initialize an array to store the vectors

    for i = 1:nVectors
        % Generate random angles
        theta = 2*pi*rand();
        phi = acos(1 - 2*rand());
        
        % Randomly adjust the magnitude within the tolerance
        adjustedMag = targetMag + (rand() - 0.5) * 2 * tolerance;
        
        % Convert to Cartesian coordinates
        x = adjustedMag * sin(phi) * cos(theta);
        y = adjustedMag * sin(phi) * sin(theta);
        z = adjustedMag * cos(phi);

        % Store the vector
        vectors(i, :) = [x, y, z];
    end
end

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Answer 2

[Bruno Luong]

MagTarget = 10;
MagRange = 0.5;
n = 1000;
m = MagTarget + MagRange * (rand(1,n)-0.5);
xyz = randn(3,n);
xyz = xyz .* (m ./ sqrt(sum(xyz.^2,1)));

xyz(:,1)

ans = 3×1

1.6927 8.0711 5.7062

norm(ans)

ans = 10.0284

xyz(:,10)

ans = 3×1

2.7756 3.0553 -8.9397

norm(ans)

ans = 9.8466