A particle is acted upon by forces F = (10N, 060º), P = (15N, 120º) and Q = (12N, 200º). Express the force that will keep the particle in equilibrium in the form xi + yj, where x and y are scalars.

  • A 17.55i + 13.78j
  • B 17.55j - 13.78i
  • C -17.55i + 13.78j
  • D -17.55i - 13.78j
waec 2022furthermathematics

The correct answer is B. 17.55j - 13.78i

Converting the forces to their rectangular forms

F = (10N, 060º)

Fx = 10cos60 = 5i

fy = 10sin60 = 8.66j

F = 5i + 8.66j

P = (15N, 120º)

Px = 15cos120 = -7.5i

py = 15sin120 = 12.99j

P = -7.5i + 12.99j

Q = (12N, 200º)

Qx = 12cos200 = -11.28i

Qy = 12sin200 = -4.1j

Q = -11.28i -4.1j

The resultant force = F + P + Q

R = 5i + 8.66j + (-7.5i + 12.99j) + (-11.28i -4.1j)

R = -13.78i + 17.55j

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