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    Coding in Matlab - Dot, cross, and triple products

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    The objective is to write MATLAB codes that calculate scalar, vector and triple (scalar) products of vectors.

    Example: the scalar product function is R^3

    Copy and paste the following programme into the MATLAB editor and save the program as scalar_prod.m

    function z = scalar_prod(x,y) % clears all the variables from memory
    z = 0; % initiate z
    for i = 1:3; % loop
    z = z+x(i)*y(i); % calculate each product and add it to the previous sum
    end; % end the loop

    To see an example of the use of the programme, return to the command window and type:
    >> x = [1; 2; 3];
    >> y = [-1; 1; 1];
    >> scalar_prod(x; y)

    You should see the answer:
    >> ans = 4


    1. Write a function to calculate the scalar product of two vectors in R^4. Test your new function with the vectors x = [3;4;2;1] and y = [-2;3;4;5].

    2. Write a function for calculating the cross product of two vectors in R^3. Test this function with the vectors x = [6;3;8] and y = [-3;2;-7].

    3. Write a function for calculating the triple (scalar) product of three vectors in R^3. Test this function with the vectors x = [1;2;3], y = [-1;8;9] and z = [-2;3;4]. What is the MATLAB function, which allows a direct computation of a triple product?

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    Solution Preview

    1. To find the scaler product of two vectors in R^4, we know each vector has exactly 4 entries. The Matlab code to extract the i-th entry for a vector x is x(i). So in your file scaler_prod.m, write:

    function p=scaler_prod(x,y)

    2. Now using the cross product formula of two vectors in R^3, in the file cross_prod.m, write:

    function c=cross_prod(x,y)

    Solution Summary

    This solution examines some basic vector operations in Matlab via working through the coding of dot and cross products.