I have opened the image you provided. Let’s proceed by drawing vector diagrams for the problems outlined. I will focus on the first three problems to start. Here's a breakdown of what the diagrams would represent:

1. Problem 1: A plane is flying due north, and wind blows it due west. We need to draw two vectors:

   • One representing the velocity of the plane (100.0 m/s north).
   • The other representing the velocity of the wind (50.0 m/s west). The resultant vector (hypotenuse) represents the resultant velocity.

2. Problem 2: A hiker walks 10.0 km north and then 10.0 km east.

   • First vector: 10.0 km due north.
   • Second vector: 10.0 km due east. The resultant vector is the direct displacement from the starting point to the endpoint.

3. Problem 3: An airplane flies due west while wind blows from the north.

   • One vector: 120.0 km/h due west.
   • The second vector: 40.0 km/h from the north. The resultant vector gives the plane's overall velocity and direction.

Let me draw these diagrams for clarity.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can provide a detailed step-by-step process to help you manually draw the vector diagrams for each problem. Let me know if you'd prefer that or have any specific questions!