Coding in Matlab - Dot, cross, and triple products
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See the attached file.
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
Tasks
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 Summary
This solution examines some basic vector operations in Matlab via working through the coding of dot and cross products.
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)
p=x(1)*y(1)+x(2)*y(2)+x(3)*y(3)+x(4)*y(4);
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)
c=zeros(3,1);
c(1)=x(2)*y(3)-y(3)*x(2);
...
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