A level south west regional mock gce 2022 further mathematics 3
A level south west regional mock gce 2022 further mathematics 3
1. a) A force F, actingparallel to the vector (—5i + 2j + 5k), displaces a particle from the point with position
vector (3£ — 3j + 4k)m to the point with position vector (i — 4j + 6k)m. Given that the work done on
the particle is 36 joules,find F.
b) Three forces Flt F2 and F3 act respectively at the points with position vectors rx,r2 andr3 such that
Fx = (t + 2j + 3k )N , rx = (J + k )m
F2 = (—i + 2k)N , r2 = (4t + j – k )m
F3 = (pi + qj +rk)N, r3 = (at + /?/ + 5k )m. Given that Fx+ F2 + F3 = 0 and that the sum of the
moments of the three forces about the origin 0 is (-7i + 9j- 6k )Nm,
(i) state the system of forces that the three forces form,
(ii) hence find the values of p,q and r,
(iii) find the moments of Fxand F2 about the origin.
(iv) Hence,determine the values of a and /?
