1. Given fields

   $\vec E = 2\hat i + 3\hat j, \qquad \vec B = 4\hat j + 6\hat k$

   The particle is moved from the origin $O(0,0)$ to point $P(1,1)$ along a straight line.

2. Work done by magnetic field

   Magnetic force is always perpendicular to velocity:

   $\vec F_B = q(\vec v \times \vec B)$

   Hence,

   $W_B = \int \vec F_B \cdot d\vec r = 0$

   So only the electric field does work.

3. Work done by electric field

   Electric force:

   $\vec F_E = q\vec E = q(2\hat i + 3\hat j)$

   Displacement from origin to $(1,1)$ is

   $\Delta \vec r = \hat i + \hat j$

   Therefore work done:

   $W = \vec F_E \cdot \Delta \vec r = q(2\hat i + 3\hat j) \cdot (\hat i + \hat j)$

   $W = q(2\cdot 1 + 3\cdot 1) = 5q$

4. Magnitude of total work done

   $|W| = 5q$

5. Option check

   • A: $(2.5)q$ ❌
   • B: $(0.35)q$ ❌
   • C: $(0.15)q$ ❌
   • D: $5q$ ✅

Therefore, the correct answer is D.