If the symmetrical form of line of intersection of planes `4x-3y=1,2y-4z=3` is
`(x-a)/(3)=(y)/(4)=(z+3//4)/(2)` then a = ___________

Answer

To find the value of \( a \) in the symmetrical form of the line of intersection of the planes given by the equations \( 4x - 3y = 1 \) and \( 2y - 4z = 3 \), we can follow these steps:

### Step 1: Rearranging the equations of the planes
We start with the equations of the planes:
1. \( 4x - 3y = 1 \)
2. \( 2y - 4z = 3 \)

From the first equation, we can express \( y \) in terms of \( x \):
\[ 3y = 4x - 1 \implies y = \frac{4x - 1}{3} \]

From the second equation, we can express \( y \) in terms of \( z \):
\[ 2y = 4z + 3 \implies y = 2z + \frac{3}{2} \]

### Step 2: Setting the two expressions for \( y \) equal
Now, we set the two expressions for \( y \) equal to each other:
\[ \frac{4x - 1}{3} = 2z + \frac{3}{2} \]

### Step 3: Cross-multiplying to eliminate the fraction
To eliminate the fraction, we can cross-multiply:
\[ 4x - 1 = 3(2z + \frac{3}{2}) \]
\[ 4x - 1 = 6z + \frac{9}{2} \]

### Step 4: Rearranging the equation
Rearranging gives us:
\[ 4x - 6z = \frac{9}{2} + 1 \]
\[ 4x - 6z = \frac{11}{2} \]

### Step 5: Finding the symmetrical form
Now, we can express \( x \), \( y \), and \( z \) in a symmetrical form. We can express \( x \) in terms of a parameter \( t \):
Let \( x = t \), then:
\[ 4t - 6z = \frac{11}{2} \implies z = \frac{4t - \frac{11}{2}}{6} \]
\[ z = \frac{2t - \frac{11}{12}}{3} \]

### Step 6: Expressing in terms of \( y \)
Now, substituting \( x = t \) into the expression for \( y \):
\[ y = \frac{4t - 1}{3} \]

### Step 7: Formulating the symmetrical equation
Now we can write the symmetrical form of the line:
\[ \frac{x - a}{3} = \frac{y}{4} = \frac{z + \frac{11}{12}}{2} \]

### Step 8: Comparing with the given form
The given symmetrical form is:
\[ \frac{x - a}{3} = \frac{y}{4} = \frac{z + \frac{3}{4}}{2} \]

From the comparison, we can see that:
\[ a = \frac{1}{4} \]

### Final Answer
Thus, the value of \( a \) is:
\[ \boxed{\frac{1}{4}} \]