Assertion: If `hat(i)` and `hat(j)` are unit Vectors along x-axis and y-axis respectively, the magnitude of Vector `hat(i)+hat(j)` will be `sqrt(2)`
Reason: Unit vectors are used to indicate a direction only.

Explanation

To solve the question, we need to analyze the assertion and the reason given:

### Step 1: Understand the Assertion
The assertion states that if \( \hat{i} \) and \( \hat{j} \) are unit vectors along the x-axis and y-axis respectively, then the magnitude of the vector \( \hat{i} + \hat{j} \) will be \( \sqrt{2} \).

### Step 2: Calculate the Magnitude of \( \hat{i} + \hat{j} \)
To find the magnitude of the vector \( \hat{i} + \hat{j} \):
1. Recognize that \( \hat{i} \) represents a unit vector in the x-direction, which can be expressed as \( (1, 0) \).
2. Similarly, \( \hat{j} \) represents a unit vector in the y-direction, which can be expressed as \( (0, 1) \).
3. Therefore, the vector \( \hat{i} + \hat{j} \) can be expressed as:
\[ \hat{i} + \hat{j} = (1, 0) + (0, 1) = (1, 1) \]

### Step 3: Use the Pythagorean Theorem to Find the Magnitude
To find the magnitude of the vector \( (1, 1) \):
\[ \text{Magnitude} = \sqrt{x^2 + y^2} = \sqrt{1^2 + 1^2} = \sqrt{1 + 1} = \sqrt{2} \]

### Step 4: Conclusion on the Assertion
The assertion is correct: the magnitude of the vector \( \hat{i} + \hat{j} \) is indeed \( \sqrt{2} \).

### Step 5: Analyze the Reason
The reason states that "unit vectors are used to indicate a direction only." This is also correct because unit vectors are defined to have a magnitude of 1 and are used to specify direction in space.

### Step 6: Relationship Between Assertion and Reason
While both the assertion and the reason are correct, the reason does not explain the assertion. The assertion is about the magnitude of the resultant vector, while the reason discusses the purpose of unit vectors.

### Final Conclusion
Both the assertion and the reason are correct, but the reason does not explain the assertion. Therefore, the answer to the question is that both statements are true, but the reason does not support the assertion.

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