The electric field in a region is given `vecE=((3)/(5)E_(0) hati+(4)/(5)E_(0) hatj)(N)/(C)`. The ratio of flux of reported field through the rectangular surface of area `0.2 m^(2)` (parallel to y - z plane) to that of the surface of area `0.3m^(2)` (parallel to x-z plane) is a:b where a= ____ [ Here `hati, hatj and hatk` are unit vectors along x,y and z-axes respectively ]

Answer

To solve the problem, we need to calculate the electric flux through two surfaces and find the ratio of these fluxes.

### Step-by-Step Solution:

1. **Identify the Electric Field**:
The electric field is given as:
\[ \vec{E} = \left(\frac{3}{5} E_0 \hat{i} + \frac{4}{5} E_0 \hat{j}\right) \, \text{N/C} \]

2. **Determine the Areas and Their Orientations**:
- The area \( A_x = 0.2 \, m^2 \) is parallel to the y-z plane. The normal vector for this surface is along the x-axis, i.e., \( \hat{i} \).
- The area \( A_y = 0.3 \, m^2 \) is parallel to the x-z plane. The normal vector for this surface is along the y-axis, i.e., \( \hat{j} \).

3. **Calculate the Electric Flux through Each Surface**:
The electric flux \( \Phi \) through a surface is given by:
\[ \Phi = \vec{E} \cdot \vec{A} \]

- **Flux through the surface parallel to the y-z plane**:
\[ \Phi_x = \vec{E} \cdot \vec{A_x} = \left(\frac{3}{5} E_0 \hat{i} + \frac{4}{5} E_0 \hat{j}\right) \cdot (0.2 \hat{i}) = \frac{3}{5} E_0 \cdot 0.2 = \frac{0.6 E_0}{5} \]

- **Flux through the surface parallel to the x-z plane**:
\[ \Phi_y = \vec{E} \cdot \vec{A_y} = \left(\frac{3}{5} E_0 \hat{i} + \frac{4}{5} E_0 \hat{j}\right) \cdot (0.3 \hat{j}) = \frac{4}{5} E_0 \cdot 0.3 = \frac{1.2 E_0}{5} \]

4. **Find the Ratio of the Fluxes**:
Now, we need to find the ratio \( \frac{\Phi_x}{\Phi_y} \):
\[ \frac{\Phi_x}{\Phi_y} = \frac{\frac{0.6 E_0}{5}}{\frac{1.2 E_0}{5}} = \frac{0.6}{1.2} = \frac{1}{2} \]

5. **Express the Ratio in Terms of a:b**:
The ratio \( \frac{\Phi_x}{\Phi_y} = \frac{1}{2} \) can be expressed as \( a:b \) where \( a = 1 \) and \( b = 2 \).

### Final Answer:
The value of \( a \) is:
\[ \boxed{1} \]