In the following questions a statement of assertion (A) is followed by a statement of reason ( R).
A: Three vectors having magnitudes 10,10 and 25 cannot produce zero resultant.
R: If three vectors are producing zero resultant then sum of magnitude of any two is more then or equal to magnitude of third and difference is less than or equal to the magnitude of third.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion then mark (1) .
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion then mark (2)
C. If Assertion is true statement but Reason is false then mark (3).
D. If both Assertion and Reason are false statements then mark (4) .

Answer

To solve the problem, we need to analyze both the assertion (A) and the reason (R) provided in the question.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that three vectors with magnitudes 10, 10, and 25 cannot produce a zero resultant.
- To check this, we need to apply the triangle inequality theorem, which states that for three sides (or vectors) to form a closed triangle (and hence produce a zero resultant), the sum of the magnitudes of any two sides must be greater than or equal to the magnitude of the third side.

2. **Applying the Triangle Inequality**:
- Let's denote the vectors as \( V_1 = 10 \), \( V_2 = 10 \), and \( V_3 = 25 \).
- We will check the triangle inequality conditions:
- \( V_1 + V_2 \geq V_3 \)
- \( V_1 + V_3 \geq V_2 \)
- \( V_2 + V_3 \geq V_1 \)

3. **Calculating the Sums**:
- Check \( V_1 + V_2 \geq V_3 \):
\[ 10 + 10 = 20 \quad \text{and} \quad 20 < 25 \quad \text{(not satisfied)} \]
- Check \( V_1 + V_3 \geq V_2 \):
\[ 10 + 25 = 35 \quad \text{and} \quad 35 \geq 10 \quad \text{(satisfied)} \]
- Check \( V_2 + V_3 \geq V_1 \):
\[ 10 + 25 = 35 \quad \text{and} \quad 35 \geq 10 \quad \text{(satisfied)} \]

4. **Conclusion on Assertion**:
- Since the first condition is not satisfied (\( 10 + 10 < 25 \)), the three vectors cannot produce a zero resultant. Thus, the assertion (A) is **true**.

5. **Understanding the Reason (R)**:
- The reason states that if three vectors are producing a zero resultant, then the sum of the magnitudes of any two must be greater than or equal to the magnitude of the third, and the difference must be less than or equal to the magnitude of the third.
- This is a correct statement as it reflects the conditions required for three vectors to produce a zero resultant.

6. **Conclusion on Reason**:
- The reason (R) is also **true** and correctly explains the assertion (A).

### Final Conclusion:
Both the assertion (A) and the reason (R) are true, and the reason correctly explains the assertion.