In an orienteering class, you have the goal of moving as far from base camp as possible by making three straight-line moves. You may use the following displacement in any order: (a) `veca,2.0` km due east (b) `vecb,2.0` km `30^(@)` north of east (c ) `vecc,` 1.0 km due west. Alternatively, you may substitude either `-vecb ` for `vecb or - vecc ` for `vec.` What is the greatest distance you can be from base camp the the end of the third displacement

Explanation

To solve the problem of maximizing the distance from the base camp after three straight-line moves, we will analyze the given displacements and calculate the resultant vector step by step.

### Step 1: Define the Displacements
We have three displacements:
1. **Vector A**: \( \vec{A} = 2.0 \, \text{km} \) due east.
2. **Vector B**: \( \vec{B} = 2.0 \, \text{km} \) at \( 30^\circ \) north of east.
3. **Vector C**: \( \vec{C} = 1.0 \, \text{km} \) due west.

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