Question

6. Consider two column vectors b azand b= [ 23 ] The dot product between a and b is given by the scalar d=a.b=a+b = 4,61 + a2b2 + a3b3. The dot product also satisfies the relationship a. b = |||||||| cos(0) where al = a.a is the length of a and is the angle between a and b. The cross product between a and b is given by the column vector c=axb= with G = aby - azby C2 = 23h - ab o = ,62 - azbi Write a script that prompts the user for two column vectors, a and b. The script should then calculate and print the dot product between a and b, the length of a, the length of b, the angle between a and b, and the cross product between a and b. Do not use the built-in functions dot or cross. Sample output: Enter column vector 1.5- 25 Enter column vector 3 3 -2.25 -6 ] The dot product of A and B 18-21 0000 The length of A la 5.5902 The length of 18 7.0755 The angle between A and B 19 2.1305 - prt sc delete $ backspace

Use octave to code and use disp to print entire vectors of numbers.

Answer 1

A=input('Enter column vector A:');
B=input('Enter column vector B:');
dotproduct=sum(A.*B);

disp(['The dot product of A and B is ', num2str(dotproduct)])
lenA=sqrt(sum(A.*A));
lenB=sqrt(sum(B.*B));
disp(['The length of A is :',num2str(lenA)]);
disp(['The length of B is :',num2str(lenB)]);
angle=rad2deg(acos(dotproduct/(lenA*lenB)))
disp(['The angle between A and B is :',num2str(angle)]);
crossprod=[A(2)*B(3)-A(3)*B(2);A(3)*B(1)-A(1)*B(3);A(1)*B(2)-A(2)*B(1)];
disp(['The cross product of A and B is '])
disp(crossprod)