In the following questions a statement of assertion (A) is followed by a statement of reason ( R).
A : The addition of two vectors `vecP ` and `vecQ` is commutative
R: By triangle law of vector addition we can prove `vecP+vecQ=vecQ+vecP` .

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 question regarding the commutativity of vector addition, we can follow these steps:

### Step-by-Step Solution:

**Step 1: Understand the Assertion and Reason**
- The assertion (A) states that the addition of two vectors \( \vec{P} \) and \( \vec{Q} \) is commutative, meaning \( \vec{P} + \vec{Q} = \vec{Q} + \vec{P} \).
- The reason (R) claims that this can be proven using the triangle law of vector addition.

**Step 2: Define the Vectors**
- Let vector \( \vec{P} \) be represented horizontally with a magnitude \( P \).
- Let vector \( \vec{Q} \) be represented vertically downwards with a magnitude \( Q \).

**Step 3: Construct the Triangle**
- Draw a triangle where one side represents \( \vec{P} \) and the other side represents \( \vec{Q} \).
- The resultant vector \( \vec{R} \) (which represents \( \vec{P} + \vec{Q} \)) can be represented as the third side of the triangle.

**Step 4: Apply the Triangle Law of Vector Addition**
- According to the triangle law, if two vectors are represented as two sides of a triangle, their sum is represented by the third side taken in the direction from the tail of the first vector to the head of the second vector.

**Step 5: Prove Commutativity**
- If we rearrange the vectors, we can also represent \( \vec{Q} \) first and then \( \vec{P} \). This forms another triangle.
- By the triangle law, the resultant vector from this arrangement (which represents \( \vec{Q} + \vec{P} \)) will have the same magnitude and direction as the resultant vector from the first arrangement (which represents \( \vec{P} + \vec{Q} \)).
- Therefore, we conclude that \( \vec{P} + \vec{Q} = \vec{Q} + \vec{P} \).

**Step 6: Conclusion**
- Since both the assertion and the reason are true and the reason correctly explains the assertion, we conclude that both statements are valid.

### Final Answer:
Both assertion (A) and reason (R) are true, and the reason is the correct explanation of the assertion.

---