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
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?
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:
2. Now using the cross product formula of two vectors in R^3, in the file cross_prod.m, write:
This solution examines some basic vector operations in Matlab via working through the coding of dot and cross products.