1.3.2 largest. Figures 4 and 5 show forces that act in the vertical plane on an object. Determine the resultant of the forces in each diagram by means of a graphical method. Give the direction of the resultant relative to the horizontal. Describe the characteristic of a vector diagram (drawn tail-to-head) in which the resultant is zero. wers to numerical questions Resultant: 87 N at $$ 13^{\circ} $$ to the horizontal; 1.1 .2 Resultant: 78 N

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To solve the problem of determining the resultant of the forces in the diagrams (Figures 4 and 5) using a graphical method, we will follow these steps:

### Step 1: Extract Known Conditions
From the problem statement, we have:
- Resultant from the first diagram: $$ R_1 = 87 \, 	ext{N} $$ at $$ 13^{\circ} $$ to the horizontal.
- Resultant from the second diagram: $$ R_2 = 78 \, 	ext{N} $$.

### Step 2: Graphical Method to Determine Resultants
1. **Draw the Vectors**: 
   - For the first resultant $$ R_1 $$:
     - Draw a vector of length proportional to $$ 87 \, 	ext{N} $$ at an angle of $$ 13^{\circ} $$ above the horizontal.
   - For the second resultant $$ R_2 $$:
     - Draw a vector of length proportional to $$ 78 \, 	ext{N} $$ (the angle is not specified, so we will assume it is horizontal unless stated otherwise).

2. **Tail-to-Head Method**:
   - Place the tail of the second vector at the head of the first vector.
   - The resultant vector will be drawn from the tail of the first vector to the head of the second vector.

### Step 3: Determine the Direction of the Resultant
To find the direction of the resultant relative to the horizontal, we can use trigonometric functions. The angle $$ 	heta $$ can be calculated using the tangent function if we have the vertical and horizontal components of the resultant.

### Step 4: Characteristics of a Vector Diagram with Zero Resultant
In a vector diagram where the resultant is zero:
- The vectors must form a closed polygon when drawn tail-to-head.
- The sum of the vectors in both the horizontal and vertical directions must equal zero.

### Conclusion
The resultant forces from the diagrams are:
- For the first diagram: $$ R_1 = 87 \, 	ext{N} $$ at $$ 13^{\circ} $$ to the horizontal.
- For the second diagram: $$ R_2 = 78 \, 	ext{N} $$ (assumed horizontal).

Now, let's summarize the results:
- **Resultant of Diagram 1**: $$ 87 \, 	ext{N} $$ at $$ 13^{\circ} $$
- **Resultant of Diagram 2**: $$ 78 \, 	ext{N} $$

If you need further calculations or graphical representations, please provide the specific angles or additional details from Figures 4 and 5.
The resultant forces are: - **Diagram 1**: 87 N at 13° to the horizontal - **Diagram 2**: 78 N

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