The net displacement of the body is
∆x = (4, 3, 3) m - (-5, 3, 1) m = (9, 0, 2) m
so the work done by F = (3, 0, 4) N in the direction of ∆x is
F • ∆x = (3, 0, 4) • (9, 0, 2) N•m = (27 + 0 + 8) N•m = 35 J
The angle between the force and initial velocity v₀ is θ, such that
F • v₀ = ||F|| ||v₀|| cos(θ)
(3, 0, 4) • (6, 1, 1) N•m/s = √(3² + 0² + 4²) √(6² + 1² + 1²) cos(θ) N•m/s
==> cos(θ) = (18 + 0 + 4) / (√25 × √38) = 22/(5√38)
==> θ = arccos(22/(5√38)) ≈ 44.5°
