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 solve the problem of finding the vector sum of the forces of 10 newton and 6 newton, we will follow these steps:

### Step 1: Identify the Forces
We have two forces:
- \( F_1 = 10 \, \text{N} \)
- \( F_2 = 6 \, \text{N} \)

### Step 2: Understand Vector Addition
The resultant force \( F_R \) can vary depending on the direction of the forces. The vector sum of two forces can be calculated using the triangle law of vector addition.

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

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

### Step 5: Determine the Range of Resultant Force
The resultant force \( F_R \) can vary between the minimum and maximum values calculated:
\[ 4 \, \text{N} \leq F_R \leq 16 \, \text{N} \]

### Step 6: Evaluate Possible Values
Now we need to check which of the provided options falls within this range. The possible values given are:
- 2 N (not in range)
- 4 N (minimum)
- 8 N (in range)
- 16 N (maximum)
- 18 N (not in range)
- 20 N (not in range)

From the options, only 8 N is within the range of 4 N to 16 N.

### Conclusion
Thus, the vector sum of the forces of 10 newton and 6 newton can be 8 newton.

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