A particle starts moving from point (2, 10, 1). Displacement for the particle is `8hati - 2hatj + hatk` . The final coordinates of the particle is

Options

A. `(10, 8, 2)`
B. `(8, 10, 2)`
C. `(2, 10, 8)`
D. `(8, 2, 10)`

Explanation

To find the final coordinates of the particle after its displacement, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial Position Vector**:
The particle starts from the point (2, 10, 1). In vector form, this can be represented as:
\[ \mathbf{r_1} = 2\hat{i} + 10\hat{j} + 1\hat{k} \]

2. **Identify the Displacement Vector**:
The displacement given is:
\[ \mathbf{d} = 8\hat{i} - 2\hat{j} + 1\hat{k} \]

3. **Set Up the Equation for Final Position Vector**:
The final position vector \( \mathbf{r_2} \) can be expressed in terms of the initial position vector and the displacement:
\[ \mathbf{r_2} = \mathbf{r_1} + \mathbf{d} \]

4. **Substitute the Values**:
Substitute the initial position vector and the displacement vector into the equation:
\[ \mathbf{r_2} = (2\hat{i} + 10\hat{j} + 1\hat{k}) + (8\hat{i} - 2\hat{j} + 1\hat{k}) \]

5. **Combine the Vectors**:
Combine the components of the vectors:
\[ \mathbf{r_2} = (2 + 8)\hat{i} + (10 - 2)\hat{j} + (1 + 1)\hat{k} \]
\[ \mathbf{r_2} = 10\hat{i} + 8\hat{j} + 2\hat{k} \]

6. **Write the Final Coordinates**:
The final coordinates of the particle are:
\[ (10, 8, 2) \]

### Final Answer:
The final coordinates of the particle are \( (10, 8, 2) \).

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