A vector perpendicular to `(4hati-3hatj)` may be :

Explanation

To find a vector that is perpendicular to the vector \( \vec{A} = 4\hat{i} - 3\hat{j} \), we can use the property that the dot product of two perpendicular vectors is zero.

### Step-by-Step Solution:

1. **Define the Perpendicular Vector**:
Let the vector we are looking for be \( \vec{B} = x\hat{i} + y\hat{j} \).

2. **Set Up the Dot Product**:
The dot product of \( \vec{A} \) and \( \vec{B} \) must equal zero for them to be perpendicular:
\[ \vec{A} \cdot \vec{B} = (4\hat{i} - 3\hat{j}) \cdot (x\hat{i} + y\hat{j}) = 0 \]

3. **Calculate the Dot Product**:
Using the properties of the dot product:
\[ \vec{A} \cdot \vec{B} = 4x + (-3)y = 4x - 3y \]
Set this equal to zero:
\[ 4x - 3y = 0 \]

4. **Rearrange the Equation**:
Rearranging gives:
\[ 4x = 3y \quad \Rightarrow \quad \frac{x}{y} = \frac{3}{4} \]

5. **Find Values for x and y**:
From the ratio \( \frac{x}{y} = \frac{3}{4} \), we can express \( x \) and \( y \) in terms of a common variable. Let \( y = 4k \) for some scalar \( k \):
\[ x = 3k \]

6. **Choose a Simple Value for k**:
To find a specific vector, we can choose \( k = 1 \):
\[ x = 3 \quad \text{and} \quad y = 4 \]

7. **Write the Perpendicular Vector**:
Thus, the vector that is perpendicular to \( 4\hat{i} - 3\hat{j} \) is:
\[ \vec{B} = 3\hat{i} + 4\hat{j} \]

### Conclusion:
The vector \( 3\hat{i} + 4\hat{j} \) is perpendicular to \( 4\hat{i} - 3\hat{j} \).