The resultant vector of of `bar(OA) = 2hati + 3hatj + 6hatk` and `bar(OB) = 2hati - 5hatj + 3hatk` is

Options

A. `4hati+9hatk`
B. `4hati+8hatj -3hatk`
C. `-2hatj+3hatk`
D. `4hati-2hatj+9hatk`

Answer

To find the resultant vector of the vectors \( \bar{OA} \) and \( \bar{OB} \), we will follow these steps:

1. **Identify the vectors**:
- \( \bar{OA} = 2\hat{i} + 3\hat{j} + 6\hat{k} \)
- \( \bar{OB} = 2\hat{i} - 5\hat{j} + 3\hat{k} \)

2. **Write the formula for the resultant vector**:
The resultant vector \( \bar{R} \) can be found by adding the two vectors:
\[ \bar{R} = \bar{OA} + \bar{OB} \]

3. **Add the vectors component-wise**:
- **i-component**:
\[ 2 + 2 = 4 \]
- **j-component**:
\[ 3 - 5 = -2 \]
- **k-component**:
\[ 6 + 3 = 9 \]

4. **Combine the components to form the resultant vector**:
Putting the components together, we get:
\[ \bar{R} = 4\hat{i} - 2\hat{j} + 9\hat{k} \]

5. **Final Result**:
The resultant vector is:
\[ \bar{R} = 4\hat{i} - 2\hat{j} + 9\hat{k} \]