Question

. Perform graphically the following vector additions and subtractions, where 𝐴⃗, 𝐵⃗⃗, and 𝐶⃗ are the
vectors as shown below:
(a) 𝐴⃗ + 𝐵⃗⃗; (b) 𝐴⃗ + 𝐵⃗⃗ + 𝐶⃗; (c) 𝐴⃗ − 𝐵⃗⃗; (d) 𝐴⃗ + 𝐵⃗⃗ − 𝐶⃗

Answer 1

To perform vector additions and subtractions graphically, follow these steps:

### (a) \( \vec{A} + \vec{B} \)

1. **Draw vector \( \vec{A} \)** starting from the origin.
2. **From the tip of \( \vec{A} \)**, draw vector \( \vec{B} \).
3. The resultant vector \( \vec{R} = \vec{A} + \vec{B} \) is drawn from the origin (where \( \vec{A} \) starts) to the tip of \( \vec{B} \).

### (b) \( \vec{A} + \vec{B} + \vec{C} \)

1. **Follow the same steps as above** to draw \( \vec{A} + \vec{B} \).
2. **From the tip of the resultant vector \( \vec{A} + \vec{B} \)**, draw vector \( \vec{C} \).
3. The final resultant vector \( \vec{R} = \vec{A} + \vec{B} + \vec{C} \) is drawn from the origin to the tip of \( \vec{C} \).

### (c) \( \vec{A} - \vec{B} \)

1. **Draw vector \( \vec{A} \)** from the origin.
2. **To subtract**, draw vector \( \vec{B} \) in the opposite direction (i.e., as \( -\vec{B} \)).
3. **From the tip of \( \vec{A} \)**, draw \( -\vec{B} \).
4. The resultant vector \( \vec{R} = \vec{A} - \vec{B} \) is drawn from the origin to the tip of \( -\vec{B} \).

### (d) \( \vec{A} + \vec{B} - \vec{C} \)

1. **Start by drawing vector \( \vec{A} \)** from the origin.
2. **Then add vector \( \vec{B} \)** by drawing it from the tip of \( \vec{A} \).
3. For the subtraction (i.e., \( -\vec{C} \)), **draw \( \vec{C} \)** in the opposite direction from the tip of the resultant \( \vec{A} + \vec{B} \).
4. The final resultant vector \( \vec{R} = \vec{A} + \vec{B} - \vec{C} \) is drawn from the origin to the tip of \( -\vec{C} \).

### Tips for Execution:

- Ensure that all vectors are drawn to scale, and use a protractor to measure angles when necessary.
- Label all vectors appropriately to keep track of which vector is which throughout the process.
- It may be helpful to use graph paper for accuracy, or a ruler and protractor for precise angle measurements.

If you can provide specific magnitudes and directions for \( \vec{A}, \vec{B}, \) and \( \vec{C} \), I can give you more precise instructions on how to graphically represent these vectors.