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### Additional Topics in Trigonometry
## Vector Addition: Geometric Approach
**Objective:**
Construct the vector \(1.1 \mathbf{b} + 1.5 \mathbf{a}\) having initial point \(P\).
**Instructions:**
- Use the tools provided to move and scale the given vectors; then don’t forget to draw the resultant vector.
**Graph/Diagram Explanation:**
In the diagram provided:
- There is a vector labeled \(1.0 \mathbf{b}\) (in blue) originating from point \(P\).
- Another vector labeled \(1.0 \mathbf{a}\) (in yellow) is shown at a different location without an initial specified point.
**Toolbox Options:**
- There are manipulable tools in the interface, including:
- A rotation tool
- A scaling tool
- A moving tool
- An eraser
These tools are designed to help in adjusting the position and magnitude of vectors to construct the desired vector graphically.
**Action Buttons:**
- Explanation button for detailed steps
- Check button to verify the construction
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This guide provides the context and necessary steps to perform vector addition using geometric methods. The vector \(1.1 \mathbf{b} + 1.5 \mathbf{a}\) is constructed by scaling and translating the given vectors utilizing the provided tools.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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