B

To calculate the electric field intensity at point C due to the point charges at A and B, we use the formula for the electric field due to a point charge:
\[ E = \frac{k \cdot |q|}{r^2} \]
where k is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)), q is the charge, and r is the distance from the charge to the point where the electric field is being calculated.

**Step 1: Calculate the distance from A to C (r_A):**
Coordinates of A: (1, 1, 2) and C: (3, 3, 3)\
Using the distance formula: \[ r_A = \sqrt{(x_C - x_A)^2 + (y_C - y_A)^2 + (z_C - z_A)^2} \]
\[ r_A = \sqrt{(3 - 1)^2 + (3 - 1)^2 + (3 - 2)^2} = \sqrt{4 + 4 + 1} = \sqrt{9} = 3 \, \text{m} \]

**Step 2: Calculate the electric field due to charge at A (E_A):**
\[ E_A = \frac{k \cdot |q_A|}{r_A^2} = \frac{(8.99 \times 10^9) \cdot (3 \times 10^{-6})}{3^2} = \frac{(8.99 \times 10^9) \cdot (3 \times 10^{-6})}{9} = 2.99 \times 10^3 \, \text{N/C} \]

**Step 3: Calculate the distance from B to C (r_B):**
Coordinates of B: (0, 3, -1) and C: (3, 3, 3)\
\[ r_B = \sqrt{(3 - 0)^2 + (3 - 3)^2 + (3 + 1)^2} = \sqrt{9 + 0 + 16} = \sqrt{25} = 5 \, \text{m} \]

**Step 4: Calculate the electric field due to charge at B (E_B):**
\[ E_B = \frac{k \cdot |q_B|}{r_B^2} = \frac{(8.99 \times 10^9) \cdot (2.5 \times 10^{-6})}{5^2} = \frac{(8.99 \times 10^9) \cdot (2.5 \times 10^{-6})}{25} = 8.99 \times 10^3 \, \text{N/C} \]

**Step 5: Determine the direction of the electric fields:**
From A to C, the electric field is directed from A to C, and from B to C, the electric field due to charge at B is directed away from B. Thus, add the magnitudes of both fields.

**Step 6: Find the resultant electric field (E_resultant):**
Adding loads vectorially (since they are aligned):
\[ E_{resultant} = E_A + E_B = 2990 + 3590 = 6580 \, \text{N/C} \]

**Conclusion:** The electric field intensity at point C is approximately 6580 N/C in the direction away from the highest positive charge, which confirms the electric field directions from A and B.
Therefore, the correct answer is B.