What is meant by the position vector of a point P?
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Practise IGCSE 0580 questions in the style of recent Extended past papers, organised by syllabus subtopic. Each set comes with an examiner-style mark scheme and a downloadable worksheet.
Everything students ask about Cambridge IGCSE 0580 Vector geometry Topical Past Papers.
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These Vector geometry Topical Past Paper Questions are written in the style of recent Cambridge IGCSE Mathematics 0580 Extended papers and grouped by the Transformations and vectors (E7.4) section of the 2025–2027 syllabus. Use them to revise the exact skills examiners test in this part of the course.
Each question is graded Easy → Medium → Hard, plus an A★ Challenge for top-grade preparation. Tap a question to mark your own answer, then unlock the examiner-style mark scheme with model solutions and examiner tips. A printable Topical Past Papers worksheet is included so you can practise offline.
Use position vectors and vector addition to describe geometrical relationships, including parallel vectors, collinearity and the midpoint of a line segment.
What is meant by the position vector of a point P?
Point A has coordinates (5, −3). Write down its position vector.
[1 mark]A and B have position vectors (2, 4) and (8, 10) respectively. Find the position vector of the midpoint M of AB.
[2 marks]P and Q have position vectors (1, 3) and (7, −5) respectively. Find the column vector PQ.
[2 marks]Vectors u = (4, 6) and v = (2, 3). Which statement is true?
OABC is a quadrilateral with O the origin. The position vector of A is a, of B is a + b, and of C is b.
Find the vector AB in terms of a and b.
[1 mark]Find the vector OC in terms of a and b. Hence describe the shape of OABC.
[2 marks]Points A, B and C have position vectors (1, 2), (4, 8) and (10, 20) respectively. Show by vector calculation whether A, B and C are collinear (lie on a straight line).
[2 marks]In triangle OAB, M is the midpoint of OA and N is the midpoint of OB. The position vector of A is a and of B is b. Show that MN is parallel to AB and find the ratio of their lengths.
[2 marks]