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

Options

A. `hat(i)+hat(j)+10hat(k)`
B. `hat(i)+hat(j)+5hat(k)`
C. `hat(i)+hat(j)`
D. `2hat(i)+4hat(j)+6hat(k)`

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 1: Identify the position vectors
The position vector of point \( P \) can be represented as:
\[ \vec{P} = 2\hat{i} + 3\hat{j} + 5\hat{k} \]
The position vector of point \( Q \) can be represented as:
\[ \vec{Q} = 3\hat{i} + 4\hat{j} + 5\hat{k} \]

### Step 2: Write the formula for displacement vector
The displacement vector \( \vec{D} \) is given by the difference between the final position vector and the initial position vector:
\[ \vec{D} = \vec{Q} - \vec{P} \]

### Step 3: Substitute the position vectors into the formula
Substituting the position vectors we identified in Step 1:
\[ \vec{D} = (3\hat{i} + 4\hat{j} + 5\hat{k}) - (2\hat{i} + 3\hat{j} + 5\hat{k}) \]

### Step 4: Perform the vector subtraction
Now, we perform the subtraction component-wise:
\[ \vec{D} = (3 - 2)\hat{i} + (4 - 3)\hat{j} + (5 - 5)\hat{k} \]
This simplifies to:
\[ \vec{D} = 1\hat{i} + 1\hat{j} + 0\hat{k} \]

### Step 5: Write the final displacement vector
Thus, the displacement vector is:
\[ \vec{D} = \hat{i} + \hat{j} \]

### Summary
The displacement vector of the particle moving from point \( P(2, 3, 5) \) to point \( Q(3, 4, 5) \) is:
\[ \vec{D} = \hat{i} + \hat{j} \]