The vector sum of the forces of 10 newton and 6 newton can be:

Options

A. 2N
B. 8N
C. 18N
D. 20N

Explanation

To find the vector sum of the forces of 10 Newton and 6 Newton, we can use the concept of vector addition. The resultant force can vary depending on the angle between the two forces. Here’s how to approach the problem step by step:

### Step 1: Understand the Concept of Vector Addition
Vectors can be added using the triangle law of vector addition or the parallelogram law. The resultant vector depends on the magnitudes of the vectors and the angle between them.

### Step 2: Identify the Forces
We have two forces:
- Force \( F_1 = 10 \, \text{N} \)
- Force \( F_2 = 6 \, \text{N} \)

### Step 3: Calculate the Minimum Resultant
The minimum resultant occurs when the two forces are acting in opposite directions. In this case, the resultant \( R_{\text{min}} \) can be calculated as:
\[ R_{\text{min}} = |F_1 - F_2| = |10 - 6| = 4 \, \text{N} \]

### Step 4: Calculate the Maximum Resultant
The maximum resultant occurs when the two forces are acting in the same direction. In this case, the resultant \( R_{\text{max}} \) can be calculated as:
\[ R_{\text{max}} = F_1 + F_2 = 10 + 6 = 16 \, \text{N} \]

### Step 5: Determine the Range of the Resultant
From the calculations above, we can conclude that the resultant force \( R \) can vary between the minimum and maximum values:
\[ 4 \, \text{N} \leq R \leq 16 \, \text{N} \]

### Conclusion
The vector sum of the forces of 10 Newton and 6 Newton can be any value between 4 Newton and 16 Newton, inclusive.

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