Which of the following is correct ?

Options

A. The acceleration vector of a particle moving with uniform velocity can never be a null vector .
B. Non-localised vector is also known as fixed vector .
C. The magnitude of the vector `(6.0 hati -3.0hatj-9 hatk)` is `sqrt136`.
D. Vector substraction is not associative in nature .

Answer

To solve the question of which statement is correct, we will analyze each statement one by one.

### Step-by-Step Solution

1. **Analyze Statement A:**
- Statement A claims that the acceleration vector of a particle moving with uniform velocity can never be a null vector.
- **Explanation:** When a particle moves with uniform velocity, its velocity does not change over time. The acceleration vector is defined as the derivative of the velocity vector with respect to time (a = dv/dt). Since the velocity is constant, the change in velocity (dv) is zero, leading to an acceleration of zero.
- **Conclusion:** This statement is **false**.

2. **Analyze Statement B:**
- Statement B states that a non-localized vector is also known as a fixed vector.
- **Explanation:** A fixed vector is one that is localized at a specific point in space, while a non-localized vector can move freely in space. These two concepts are fundamentally different.
- **Conclusion:** This statement is **false**.

3. **Analyze Statement C:**
- Statement C claims that the magnitude of a certain vector is the square root of 136.
- **Explanation:** To find the magnitude of a vector given in component form (i, j, k), we use the formula:
\[ \text{Magnitude} = \sqrt{x^2 + y^2 + z^2} \]
If we assume the vector components are (6, 3, 9), we calculate:
\[ \text{Magnitude} = \sqrt{6^2 + 3^2 + 9^2} = \sqrt{36 + 9 + 81} = \sqrt{126} \]
Since \(\sqrt{126} \neq \sqrt{136}\), this statement is incorrect.
- **Conclusion:** This statement is **false**.

4. **Analyze Statement D:**
- Statement D states that vector subtraction is not associative in nature.
- **Explanation:** The associative property states that for any three vectors \(a\), \(b\), and \(c\):
\[ (a - b) - c \neq a - (b - c) \]
If we expand both sides, we see that they are not equal. Thus, vector subtraction does not satisfy the associative property.
- **Conclusion:** This statement is **true**.

### Final Answer
The correct statement is **D**: Vector subtraction is not associative in nature.