If `vec(A)` is `2hat(i)+9hat(j)+4hat(k)`, then `4vec(A)` will be `:`

Options

A. `8hat(i)+16hat(j)+36hat(k)`
B. `8hat(i)+36hat(k)+16hat(j)`
C. `8hat(i)+9hat(j)+16hat(k)`
D. `8hat(i)+36hat(j)+16hat(k)`

Explanation

To solve the problem, we need to find \( 4\vec{A} \) given that \( \vec{A} = 2\hat{i} + 9\hat{j} + 4\hat{k} \).

### Step-by-step Solution:

1. **Identify the vector components**:
We have the vector \( \vec{A} \) expressed in terms of its components:
\[ \vec{A} = 2\hat{i} + 9\hat{j} + 4\hat{k} \]
Here, the components are:
- \( A_x = 2 \) (coefficient of \( \hat{i} \))
- \( A_y = 9 \) (coefficient of \( \hat{j} \))
- \( A_z = 4 \) (coefficient of \( \hat{k} \))

2. **Multiply the vector by the scalar**:
To find \( 4\vec{A} \), we multiply each component of \( \vec{A} \) by 4:
\[ 4\vec{A} = 4(2\hat{i}) + 4(9\hat{j}) + 4(4\hat{k}) \]

3. **Calculate each component**:
- For the \( \hat{i} \) component:
\[ 4 \times 2 = 8 \]
- For the \( \hat{j} \) component:
\[ 4 \times 9 = 36 \]
- For the \( \hat{k} \) component:
\[ 4 \times 4 = 16 \]

4. **Combine the results**:
Now, we can combine the results to express \( 4\vec{A} \):
\[ 4\vec{A} = 8\hat{i} + 36\hat{j} + 16\hat{k} \]

### Final Answer:
Thus, \( 4\vec{A} = 8\hat{i} + 36\hat{j} + 16\hat{k} \).

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