plumiAngles with the scalar product: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on F.3 Angles with the scalar product, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 11 questions on Angles with the scalar product, as a list
- June 2025, Paper 2, Q1 (1 mark): The vectors a b and 1 c are perpendicular. Which one of the following statements must be true? Tick () one box. [1 mark] a = bc b = ac a = –b
- June 2024, Paper 1, Q12 (10 marks): The line L1 has equation r = 4 2 1 + λ 1 3 –1 The transformation T is represented by the matrix 2 1 0 3 4 6 –5 2 –3 The transformation T transforms the line L1
- June 2024, AS Paper 1, Q5 (5 marks): The vectors a and b are given by a = 3i + 4j – 2k and b = 2i – j – 5k 5 (a) Calculate a.b [1 mark] �������������������������������������������������������������
- June 2023, AS Paper 1, Q2 (1 mark): The two vectors a and b are such that a.b = 0 State the angle between the vectors a and b Circle your answer. [1 mark] 0° 45° 90° 180°
- June 2022, Paper 1, Q10 (12 marks): In this question all measurements are in centimetres. A small, thin laser pen is set up with one end at A(7, 2, −3) and the other end at B(9, −3, −2) A laser be
- June 2022, AS Paper 1, Q7 (9 marks): The lines l1 and l2 have equations l1 : r = 3 1 −2 2 664 3 775 + l 3 −4 1 2 664 3 775 l2 : r = −12 a −3 2 664 3 775 + m 3 2 −1 2 664 3 775 7 (a) Show that the p
- November 2021, Paper 1, Q11 (12 marks): The line L1 has equation r = 2 2 3 2 64 3 75 + l 2 3 −1 2 64 3 75 The line L2 has equation r = 6 4 1 2 64 3 75 + m −2 1 1 2 64 3 75 11 (a) Find the acute angle
- November 2021, Paper 2, Q3 (1 mark): The line L has equation r = 3 2 0 2 64 3 75 + l −1 −2 5 2 64 3 75 Which of the following lines is perpendicular to the line L? Tick (3) one box. [1 mark] r = 2
- November 2021, AS Paper 1, Q5 (2 marks): Show that the vectors 1 −3 5 2 64 3 75 and 7 4 1 2 64 3 75 are perpendicular. [2 marks]
- June 2019, Paper 1, Q5 (3 marks): A plane has equation r. 1 1 1 2 64 3 75 = 7 A line has equation r = 2 0 1 2 64 3 75 + m 1 0 1 2 64 3 75 Calculate the acute angle between the line and the plane
- June 2019, AS Paper 1, Q13 (10 marks): Line l1 has Cartesian equation x − 3 = 2y + 2 3 = 2 − z 13 (a) Write the equation of line l1 in the form r = a + lb where l is a parameter and a and b are vecto
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