Two vectors A and B are given as `A=(hati+5hatj)` and `B=(9hati+2hatj)`. Find the vector `(A+B)`

Answer

To find the vector \( A + B \), we will follow these steps:

### Step 1: Write down the given vectors
The vectors are given as:
- \( A = \hat{i} + 5\hat{j} \)
- \( B = 9\hat{i} + 2\hat{j} \)

### Step 2: Add the vectors component-wise
To add the vectors \( A \) and \( B \), we will add their corresponding components:
- The \( \hat{i} \) components:
\[ 1 + 9 = 10 \]
- The \( \hat{j} \) components:
\[ 5 + 2 = 7 \]

### Step 3: Write the resultant vector
Now, we can combine the results from the previous step:
\[ A + B = (10\hat{i} + 7\hat{j}) \]

### Final Answer
Thus, the vector \( A + B \) is:
\[ A + B = 10\hat{i} + 7\hat{j} \]

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