Velocity of a particle is `v=(2hat i + 3hat j - 4hat k) m//s` and its acceleration is zero. State whether it is 1-D, 2-D or 3-D motion?

Explanation

To determine whether the motion of the particle is 1-D, 2-D, or 3-D, we can analyze the given information step by step.

### Step-by-Step Solution:

1. **Identify the Velocity Vector**:
The velocity of the particle is given as:
\[ \mathbf{v} = 2\hat{i} + 3\hat{j} - 4\hat{k} \, \text{m/s} \]
This vector has components in the i, j, and k directions.

2. **Understand the Acceleration**:
The problem states that the acceleration of the particle is zero. This means that the particle is not changing its velocity.

3. **Determine the Nature of Motion**:
- Since the acceleration is zero, the particle will continue to move in the direction of its velocity vector without changing speed or direction.
- The velocity vector has components in all three dimensions (x, y, and z), indicating that it is moving in a three-dimensional space.

4. **Analyze the Motion**:
- Although the velocity vector has components in three dimensions, the particle is moving along a straight line defined by the direction of the velocity vector.
- The motion can be considered as 1-D because the particle is not changing its path; it is moving along a single straight line in 3D space.

5. **Conclusion**:
Therefore, the motion of the particle is classified as **1-D motion** because it is moving along a straight line, despite being in a three-dimensional space.

### Final Answer:
The motion is 1-D.

---