1. Create a Python program which does the following from inputting vectors v and w. Use functions in the process. (a) The program should determine if the two vectors have the same dimension. If it does, the program will proceed. Otherwise the program will ask the user to correct the mistake. (b) The program should output (v and wl. (c) The program should output the unit vectors with the same direction as v and w. (d) If the dimensions match, the program will output v +w. (e) If the dimensions match, the program will output v - w. (f) If the dimensions match, the program will output 2v. (g) If the dimensions match, the program will output 3w. (h) If the dimensions match, the program will output 3v 2w. (i) If the dimensions match, the program will output v.w. 6) If the dimensions match, the program will determine the cosine of the angle between the two vectors. (k) If the dimensions match, the program will determine if the two vectors are orthog- onal. (1) If the dimensions are appropriate, the program will output v xw. 2. Write a Python program that inputs two points in 2-space and generates an equation of any line containing the two points. 3. Write a Python program that inputs three points in 3-space and generates an equation of any plane containing these three points. If the three points are co-linear, adjust the program to inform the user. 4. (Extra Credit points) Create a Python graphical user interface which allows students to do all of the above and graphs the objects of study