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 \(\bar{OA} = 2\hat{i} + 3\hat{j} + 6\hat{k}\) and \(\bar{OB} = 2\hat{i} - 5\hat{j} + 3\hat{k}\), we will follow these steps:

### Step 1: Write down the vectors
We have two vectors:
- \(\bar{OA} = 2\hat{i} + 3\hat{j} + 6\hat{k}\)
- \(\bar{OB} = 2\hat{i} - 5\hat{j} + 3\hat{k}\)

### Step 2: Add the vectors component-wise
To find the resultant vector \(\bar{R}\), we will add the corresponding components of \(\bar{OA}\) and \(\bar{OB}\):

\[ \bar{R} = \bar{OA} + \bar{OB} \]

This can be broken down into components:

- **i-component**: \(2 + 2 = 4\)
- **j-component**: \(3 + (-5) = 3 - 5 = -2\)
- **k-component**: \(6 + 3 = 9\)

### Step 3: Write the resultant vector
Now, we can combine the components to write the resultant vector:

\[ \bar{R} = 4\hat{i} - 2\hat{j} + 9\hat{k} \]

### Final Result
Thus, the resultant vector is:

\[ \bar{R} = 4\hat{i} - 2\hat{j} + 9\hat{k} \]

---