If a particle moves from point `P(2,3,5)` to point `Q(3,4,5)`. Its displacement vector be

Options

A. `hati+hatj+10hatk`
B. `hati+hatj+5hatk`
C. `hati+hatj`
D. `2hati+4hatj+6hatk`

Explanation

To find the displacement vector of a particle moving from point \( P(2, 3, 5) \) to point \( Q(3, 4, 5) \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Coordinates of Points P and Q:**
- Point \( P \) has coordinates \( (2, 3, 5) \).
- Point \( Q \) has coordinates \( (3, 4, 5) \).

2. **Write the Displacement Vector Formula:**
- The displacement vector \( \vec{D} \) is given by the formula:
\[ \vec{D} = \vec{Q} - \vec{P} \]
- This means we subtract the coordinates of point \( P \) from the coordinates of point \( Q \).

3. **Subtract the Coordinates:**
- The coordinates of \( Q \) are \( (3, 4, 5) \) and the coordinates of \( P \) are \( (2, 3, 5) \).
- Therefore, we calculate:
\[ \vec{D} = (3 - 2) \hat{i} + (4 - 3) \hat{j} + (5 - 5) \hat{k} \]

4. **Perform the Calculations:**
- Calculate each component:
- \( 3 - 2 = 1 \)
- \( 4 - 3 = 1 \)
- \( 5 - 5 = 0 \)
- Thus, the displacement vector becomes:
\[ \vec{D} = 1 \hat{i} + 1 \hat{j} + 0 \hat{k} \]

5. **Simplify the Displacement Vector:**
- Since the \( k \) component is zero, we can write:
\[ \vec{D} = \hat{i} + \hat{j} \]

### Final Answer:
The displacement vector from point \( P \) to point \( Q \) is:
\[ \vec{D} = \hat{i} + \hat{j} \]

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