1. Calculate the acceleration:

* Force (F) = mass (m) * acceleration (a)

* a = F/m

* Substitute the given values: a = (4i + 8j + 10k) N / 3 kg

* a = (4/3)i + (8/3)j + (10/3)k m/s²

2. Calculate the velocity:

* Velocity (v) = initial velocity (u) + acceleration (a) * time (t)

* Since the particle starts from rest, u = 0

* Substitute the values: v = 0 + [(4/3)i + (8/3)j + (10/3)k m/s²] * 3 s

* v = 4i + 8j + 10k m/s

3. Calculate the displacement:

* Displacement (s) = initial position (s₀) + initial velocity (u) * time (t) + (1/2) * acceleration (a) * time² (t²)

* Since the particle starts at the origin, s₀ = 0

* Substitute the values: s = 0 + 0 * 3 s + (1/2) * [(4/3)i + (8/3)j + (10/3)k m/s²] * (3 s)²

* s = 6i + 12j + 15k m

Therefore, the new coordinates of the particle after 3 seconds will be (6, 12, 15).