Final answer:
The work done by a constant force F in moving a particle from position r1 to r2 is calculated through the dot product of the force and the displacement vectors, resulting in 29 Joules of work.
Step-by-step explanation:
The student wants to calculate the work done by a constant force F when moving a particle from position r1 to position r2. This can be determined using the dot product (also known as scalar product) between the force vector and the displacement vector. The displacement vector is derived from the initial and final positions of the particle.
We calculate the displacement vector, Δr, as r2 - r1:
Δr = (3i + 5j + k)m - (2i - j + 4k)m
Δr = (1i + 6j - 3k)m
Now, we perform the dot product of the force vector and displacement vector to find the work done (W):
W = F ⋅ Δr
W = (5i + 3j - 2k)N ⋅ (1i + 6j - 3k)m
W = 5×1 + 3×6 - 2×-3
W = 5 + 18 + 6
W = 29 Joules
Therefore, the work done by the force in moving the particle from position r1 to r2 is 29 Joules.