Vector Calculus I: Spring-2022
HW5 : Due Day 13 5/9

1. Sailing distance S0 4381S
   1. You sail 3 nautical miles \( 10^{\circ}\) north of west and 7 nautical miles due north.

      • Construct vectors that model the legs of your journey.

      • How far are you from where you started?

   2. Time to head back
      • Construct a vector that represents your return trip.
      • Add the three vectors you have constructed.
      • Explain why the sum is reasonable in terms a sailor can understand.
2. Vectors S0 4381S Find a single vector with all of the following properties:
   1. Magnitude 10
   2. Angle of \(45^\circ\) with positive \(x\)-axis
   3. Angle of \(60^\circ\) with positive \(y\)-axis
   4. Positive \(z\)-component
3. The Cube S0 4381S Find the angle between the diagonal of a cube (connecting opposite corners) and the diagonal of one of its faces (connecting opposite corners of one square face).