Find the value of p if the lines, whose equations are `2x - y + 5 = 0` and `px + 3y = 4` are perpendicular to each other. 

Answer

To find the value of \( p \) for which the lines represented by the equations \( 2x - y + 5 = 0 \) and \( px + 3y = 4 \) are perpendicular, we will follow these steps:

### Step 1: Identify the slopes of the lines
The first step is to convert both equations into the slope-intercept form \( y = mx + c \), where \( m \) is the slope.

**For the first equation:**
\[ 2x - y + 5 = 0 \]
Rearranging gives:
\[ y = 2x + 5 \]
Thus, the slope \( m_1 \) of the first line is \( 2 \).

**For the second equation:**
\[ px + 3y = 4 \]
Rearranging gives:
\[ 3y = -px + 4 \]
Dividing through by \( 3 \):
\[ y = -\frac{p}{3}x + \frac{4}{3} \]
Thus, the slope \( m_2 \) of the second line is \( -\frac{p}{3} \).

### Step 2: Use the condition for perpendicular lines
For two lines to be perpendicular, the product of their slopes must equal \(-1\):
\[ m_1 \cdot m_2 = -1 \]
Substituting the slopes we found:
\[ 2 \cdot \left(-\frac{p}{3}\right) = -1 \]

### Step 3: Solve for \( p \)
Now, we can solve the equation:
\[ -\frac{2p}{3} = -1 \]
Multiplying both sides by \(-1\):
\[ \frac{2p}{3} = 1 \]
Now, multiply both sides by \( 3 \):
\[ 2p = 3 \]
Finally, divide by \( 2 \):
\[ p = \frac{3}{2} \]

### Conclusion
The value of \( p \) for which the lines are perpendicular is:
\[ \boxed{\frac{3}{2}} \]