1. Two numbers are said to be relatively prime if they have no factors in common. Write a Python program that prompts the user to enter two integers and then prints a message saying whether or not the numbers are relatively prime.

Here are a couple of example runs:

Enter a: 49
Enter b: 12
49 and 12 are relatively prime.

Enter a: 49
Enter b: 84
49 and 84 are not relatively prime.

2. Given a set of three perpendicular vectors u₁, u₂, and u₃ in ℝ³, the coordinates of any other vector v in that space are the numbers c₁, c₂, and c₃ such that

v = c₁ u₁ + c₂ u₂ + c₃ u₃

These coordinates can be computed via the formula

Write a Python program that reads the vectors u₁, u₂, u₃ and v from a file and then computes and prints the coordinates c₁, c₂ and c₃ of v.

For example, if the file looks like

1 1 -1
1 -2 -1
-1 0 -1
4 -1 -6

Your program should print

3.0 2.0 1.0