Which of the four arrangements in the figure correctly shows the vector addition of two forces `vecF_(1)` and `vecF_(2)` to yield the third force `vecF_(3)`

Options

A.
B.
C.
D.

Answer

To determine which of the four arrangements correctly shows the vector addition of two forces \( \vec{F}_1 \) and \( \vec{F}_2 \) to yield the third force \( \vec{F}_3 \), we can follow these steps:

### Step 1: Understand Vector Addition
Vector addition involves placing the tail of one vector at the head of another vector. The resultant vector is drawn from the tail of the first vector to the head of the second vector.

### Step 2: Analyze Each Arrangement
We need to analyze each of the four arrangements provided in the figure to see which one follows the rules of vector addition.

1. **Arrangement A**: Check if \( \vec{F}_1 \) is placed at the tail of \( \vec{F}_2 \) and the resultant \( \vec{F}_3 \) is drawn from the tail of \( \vec{F}_1 \) to the head of \( \vec{F}_2 \).
2. **Arrangement B**: Check if \( \vec{F}_2 \) is placed at the tail of \( \vec{F}_1 \) and the resultant \( \vec{F}_3 \) is drawn from the tail of \( \vec{F}_2 \) to the head of \( \vec{F}_1 \).
3. **Arrangement C**: Check if \( \vec{F}_1 \) and \( \vec{F}_2 \) are drawn in such a way that \( \vec{F}_3 \) does not represent the resultant.
4. **Arrangement D**: Check if \( \vec{F}_3 \) is drawn incorrectly or does not follow the vector addition rule.

### Step 3: Identify the Correct Arrangement
After analyzing each arrangement, identify which one correctly represents the vector addition of \( \vec{F}_1 \) and \( \vec{F}_2 \) to yield \( \vec{F}_3 \).

### Conclusion
The correct arrangement will show that \( \vec{F}_1 + \vec{F}_2 = \vec{F}_3 \), meaning the head of \( \vec{F}_1 \) or \( \vec{F}_2 \) should meet the tail of \( \vec{F}_3 \).