3. For the same magnitude and direction of the vectors that you choose, perform theL d theoretical calculation, and record all your data up to three significant figures in the following table. Calculated Data: Magnitude () Direction () X- Component Y– Component V2 ーら
3. For the same magnitude and direction of the vectors that you choose, perform theL d theoretical calculation, and record all your data up to three significant figures in the following table. Calculated Data: Magnitude () Direction () X- Component Y– Component V2 ーら
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#3 please
(Use info from #2)
![### Vector Analysis and Error Calculation
#### 3. Vector Calculation Table
For the same magnitude and direction of the vectors that you choose, perform the theoretical calculation, and record all your data up to three significant figures in the following table:
| | Magnitude ( \| \vec{v} \| ) | Direction ( ° ) | X - Component | Y - Component |
|-----------------------|-----------------------------|------------------|--------------------|--------------------|
| \vec{v}_1 | | | | |
| \vec{v}_2 | | | | |
| \vec{v}_3 | | | | |
| \sum \vec{v} | | | | |
#### 4. Percent Error Calculation
Record percent error on magnitude and direction comparing your theoretical calculation (actual) and simulated data (experimental) using the formula given below:
\[ \text{Percent Error} = \left| \frac{\text{Experimental} - \text{Actual}}{\text{Actual}} \right| \times 100\% \]
(a) Percent error on magnitude of sum = _______________
(b) Percent error on direction = _______________
#### Show your calculations in the space below.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb24baab-a4c3-47eb-b813-ccb1eb59e33e%2Ffdcc3270-c35d-422b-90dd-8affe91cf9df%2Fpxfqcbl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Vector Analysis and Error Calculation
#### 3. Vector Calculation Table
For the same magnitude and direction of the vectors that you choose, perform the theoretical calculation, and record all your data up to three significant figures in the following table:
| | Magnitude ( \| \vec{v} \| ) | Direction ( ° ) | X - Component | Y - Component |
|-----------------------|-----------------------------|------------------|--------------------|--------------------|
| \vec{v}_1 | | | | |
| \vec{v}_2 | | | | |
| \vec{v}_3 | | | | |
| \sum \vec{v} | | | | |
#### 4. Percent Error Calculation
Record percent error on magnitude and direction comparing your theoretical calculation (actual) and simulated data (experimental) using the formula given below:
\[ \text{Percent Error} = \left| \frac{\text{Experimental} - \text{Actual}}{\text{Actual}} \right| \times 100\% \]
(a) Percent error on magnitude of sum = _______________
(b) Percent error on direction = _______________
#### Show your calculations in the space below.
Transcribed Image Text:### Vectors Measurement and Analysis
#### Instructions:
1. **Select three vectors** and construct a vector diagram showing their components and resultant vector. Follow the example diagram provided. You may choose your own magnitudes and directions for each vector.
2. **Record your data** in the following table.
#### Simulated Data:
The provided table and diagram detail the measurements and direction of the selected vectors.
##### Table of Magnitude and Components:
| **Vector** | \( V_1 \) | \( V_2 \) | \( V_3 \) |
|------------|-----------|-----------|-----------|
| Magnitude (\( \| \)) | 20.6 | 15.5 | 11.2 (unit) | 26.1 |
| **Direction ( degrees ) Related to** |
| @ x-axis | 5 | 5 | 10 |
| **X-Component** | 4 | 3.96 | |
| **Y-Component** | -15 | 11.02 | 5 |
*Notes: V1 and V2 have components specified. The magnitude and direction fields need full values.*
#### Explaining the Diagram:
The provided diagram shows a vector addition scenario where multiple vectors (V1, V2, and V3) are plotted with their respective components on a cartesian plane.
1. The coordinate system is marked with axes, where the black arrow signifies the \( X \) and \( Y \) directions.
2. Vectors:
- **V1**: Initiates at the 0-point, angling from the x-axis, depicted in purple.
- **V2**: Initiates from the end of V1, depicted in blue angling differently.
- **V3**: Begins from V2’s end, depicted in pink.
3. Directions and lengths are marked consistently against the grid lines with each crossing the magnitude as distance traversed.
4. Resultant vector \( \| R \| = 20.6\) is plotted showcasing the accumulated resultant direction starting from the origin of V1 to the endpoint of V3.
#### Visualization of Components:
Components are broken down to show their perpendicular contributions along the x-axis and y-axis. Legends indicate vector sum and effective contributors using respective colored arrows.
These recorded and visualized methods assist learners in understanding vector analysis's fundamental
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