Find the sum of the vectors ` 10hati + 6hatj and 4hati - 2hatj`

Answer

To find the sum of the vectors \( \vec{A} = 10 \hat{i} + 6 \hat{j} \) and \( \vec{B} = 4 \hat{i} - 2 \hat{j} \), we will follow these steps:

### Step 1: Identify the components of each vector
- For vector \( \vec{A} \):
- The \( \hat{i} \) component is 10.
- The \( \hat{j} \) component is 6.

- For vector \( \vec{B} \):
- The \( \hat{i} \) component is 4.
- The \( \hat{j} \) component is -2.

### Step 2: Add the \( \hat{i} \) components
To find the \( \hat{i} \) component of the resultant vector \( \vec{R} \):
\[ \text{Resultant } \hat{i} \text{ component} = 10 + 4 = 14 \]

### Step 3: Add the \( \hat{j} \) components
To find the \( \hat{j} \) component of the resultant vector \( \vec{R} \):
\[ \text{Resultant } \hat{j} \text{ component} = 6 + (-2) = 6 - 2 = 4 \]

### Step 4: Write the resultant vector
Combining the \( \hat{i} \) and \( \hat{j} \) components, we get:
\[ \vec{R} = 14 \hat{i} + 4 \hat{j} \]

### Final Answer
The sum of the vectors \( \vec{A} + \vec{B} \) is:
\[ \vec{R} = 14 \hat{i} + 4 \hat{j} \]

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