Which one of the following cannot be the resultant of the vectors of magnitude 5 and 10 ?

Options

A. 7
B. 8
C. 5
D. 2

Explanation

To determine which resultant cannot be obtained from vectors of magnitudes 5 and 10, we can use the properties of vector addition.

### Step-by-Step Solution:

1. **Identify the Magnitudes of the Vectors**:
We have two vectors, \( P \) and \( Q \), with magnitudes \( |P| = 5 \) and \( |Q| = 10 \).

2. **Determine the Range of Possible Resultants**:
The resultant \( R \) of two vectors can vary depending on the angle \( \theta \) between them. The formula for the magnitude of the resultant \( R \) is given by:
\[ R = \sqrt{P^2 + Q^2 + 2PQ \cos \theta} \]
where \( P = 5 \) and \( Q = 10 \).

3. **Calculate Maximum Resultant**:
- When the vectors are in the same direction (\( \theta = 0^\circ \)):
\[ R_{\text{max}} = P + Q = 5 + 10 = 15 \]

4. **Calculate Minimum Resultant**:
- When the vectors are in opposite directions (\( \theta = 180^\circ \)):
\[ R_{\text{min}} = |P - Q| = |5 - 10| = 5 \]

5. **Establish the Range of Possible Resultants**:
The resultant \( R \) can take any value in the range:
\[ 5 \leq R \leq 15 \]

6. **Identify the Impossible Resultant**:
Now, we need to identify which of the given options cannot be a resultant. Since the resultant can only be between 5 and 15, any value outside this range is not possible.

If the options are, for example: 2, 5, 10, 15, the value that cannot be the resultant is:
- **2** (since it is less than the minimum resultant of 5).

### Conclusion:
The resultant that cannot be obtained from vectors of magnitudes 5 and 10 is **2**.