Explain how you would determine how much error there is between a vector addition and the real results.

To determine the amount of error between a vector addition and the real results, you can follow these steps:

1. Identify the vector addition: Start by clearly defining the vector addition operation you are performing. For example, if you are adding two vectors A and B, denoted as A + B, make sure you have the correct vectors and their magnitudes and directions.

2. Compute the actual result: Use the correct mathematical formula or technique to calculate the vector addition accurately. This step requires properly adding the magnitudes and directions of the given vectors.

3. Calculate the error: Once you have the actual result, compare it with the expected or desired result. The error can be quantified using various methods, such as absolute error or relative error.

a. Absolute error: Subtract the actual result from the expected result, taking into account both magnitudes and directions. The absolute error is the magnitude of this difference vector. It provides a measure of how far apart the actual and expected results are without considering the scale.

b. Relative error: Divide the absolute error by the magnitude of the expected result. This ratio expresses the error in terms of a percentage or a decimal value. The relative error allows for a comparison between different calculations performed with different magnitudes.

4. Analyze the error: Finally, interpret the error value you obtained. If the error is close to zero, it means the vector addition is accurate. Conversely, if the error is large, it indicates a significant discrepancy between the vector addition and the true results.

Keep in mind that determining the error between a vector addition and the real results requires precise calculations and an understanding of vector operations. Continuous practice and the implementation of proper mathematical techniques will improve accuracy in calculating and evaluating the error.