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 the assertion (A) and the reason (R) given 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.
- For three vectors to produce a zero resultant, they must satisfy the triangle inequality conditions.

2. **Triangle Inequality Conditions**:
- The triangle inequality states that for any three sides (or vectors) A, B, and C, the following must hold:
- \( |A + B| \geq |C| \) (the sum of the magnitudes of any two vectors must be greater than or equal to the magnitude of the third vector)
- \( |A - B| \leq |C| \) (the difference of the magnitudes of any two vectors must be less than or equal to the magnitude of the third vector)

3. **Applying Triangle Inequality to the Given Vectors**:
- Let’s denote the vectors as \( A = 10 \), \( B = 10 \), and \( C = 25 \).
- Check the first condition:
- \( A + B = 10 + 10 = 20 \)
- Compare with \( C \): \( 20 < 25 \) (fails the condition)
- Check the second condition:
- Calculate \( |A - B| = |10 - 10| = 0 \)
- Compare with \( C \): \( 0 \leq 25 \) (satisfies the condition)

4. **Conclusion from the Assertion**:
- Since the first condition fails (the sum of the two vectors is not greater than or equal to the third), the assertion is correct: three vectors with magnitudes 10, 10, and 25 cannot produce a zero resultant.

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 vector, and the difference must be less than or equal to the magnitude of the third vector.
- This is indeed a correct statement regarding vector addition and the conditions for a zero resultant.

6. **Conclusion from the Reason**:
- The reason correctly explains why the assertion is true.

### Final Conclusion:
Both the assertion (A) and the reason (R) are correct. Thus, the answer to the question is that the assertion is true and the reason is a correct explanation of the assertion.