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Coding in Matlab - Dot, cross, and triple products

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?

Attachments

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);
...

Solution Summary

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

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