To perform vector additions and subtractions graphically, follow these steps:
(a) \( \vec{A} + \vec{B} \)
- Draw vector \( \vec{A} \) starting from the origin.
- From the tip of \( \vec{A} \), draw vector \( \vec{B} \).
- 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) \( \vec{A} + \vec{B} + \vec{C} \)
- Follow the same steps as above to draw \( \vec{A} + \vec{B} \).
- From the tip of the resultant vector \( \vec{A} + \vec{B} \), draw vector \( \vec{C} \).
- The final resultant vector \( \vec{R} = \vec{A} + \vec{B} + \vec{C} \) is drawn from the origin to the tip of \( \vec{C} \).
(c) \( \vec{A} - \vec{B} \)
- Draw vector \( \vec{A} \) from the origin.
- To subtract, draw vector \( \vec{B} \) in the opposite direction (i.e., as \( -\vec{B} \)).
- From the tip of \( \vec{A} \), draw \( -\vec{B} \).
- The resultant vector \( \vec{R} = \vec{A} - \vec{B} \) is drawn from the origin to the tip of \( -\vec{B} \).
(d) \( \vec{A} + \vec{B} - \vec{C} \)
- Start by drawing vector \( \vec{A} \) from the origin.
- Then add vector \( \vec{B} \) by drawing it from the tip of \( \vec{A} \).
- For the subtraction (i.e., \( -\vec{C} \)), draw \( \vec{C} \) in the opposite direction from the tip of the resultant \( \vec{A} + \vec{B} \).
- 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.