[Edexcel M1 May 2009 Q2a]

A particle is acted upon by two forces F₁ and F₂ , given by

F₁ = (i – 3j) N,

F₂ = ( pi + 2pj) N, where p is a positive constant.

Find the angle between F₂ and j.

(2 marks)

[Edexcel M1 May 2009 Q2b]

A particle is acted upon by two forces F₁ and F₂ , given by

F₁ = (i – 3j) N,

F₂ = ( pi + 2pj) N, where p is a positive constant.

The resultant of F₁ and F₂ is R.

Given that R is parallel to i, find the value of p.

(4 marks)

[Edexcel M1 June 2017 Q7a]

[In this question i and j are horizontal unit vectors due east and due north respectively and position vectors are given relative to a fixed origin O.]

Two ships, P and Q, are moving with constant velocities.

The velocity of P is (9i – 2j) km h^–1 and the velocity of Q is (4i + 8j) km h^–1

Find the direction of motion of P, giving your answer as a bearing to the nearest degree.

(3 marks)