Vector Geometry Problems · CSEC Mathematics

49 past-paper questions on Vector Geometry Problems, part of VECTORS AND MATRICES, from every CSEC Mathematics paper on Quelpr.

1. 13(b)(ii)2 marks· CSEC Mathematics · 2003 (Specimen) · Paper 2Use the results of (d) and (f) above to prove that S, R and T lie in a straight line.
2. 10(c)(i)2 marks· CSEC Mathematics · 2021 · Paper 2\vec{CD}
3. 10(c)(ii)2 marks· CSEC Mathematics · 2021 · Paper 2\vec{OE}
4. 10(c)(ii)b)3 marks· CSEC Mathematics · 2022 · Paper 2Using a vector method, show that the ratio YM : YA is 1 : 3. Show ALL working.
5. 10(b)(ii)3 marks· Mathematics Q10 10(b)(ii)Given that OX + OY = k(r + s), where k is a constant, using a vector method, find the value of k.
6. 10(b)(iii)3 marks· Mathematics Q10 10(b)(iii)Prove that R, M and T are collinear.
7. 11(a)(i)1 mark· Mathematics Q11 11(a)(i)Express MK in terms of u and v.
8. 11(a)(ii)2 marks· Mathematics Q11 11(a)(ii)Using a vector method, show that AC and OB are parallel.
9. 11(a)(ii)1 mark· Mathematics Q11 11(a)(ii)Show that OQ is parallel to RS, giving a reason for your answer.
10. 11(a)(ii)2 marks· Mathematics Q11 11(a)(ii)Express SL in terms of u and v.
11. 11(a)(ii)3 marks· Mathematics Q11 11(a)(ii)Hence, determine whether A, B and C are collinear, giving the reasons for your answer.
12. 11(a)(ii)2 marks· Mathematics Q11 11(a)(ii)State TWO geometrical relationships that exist between OB and PQ. Give reasons for your answers.
13. 11(a)(ii)1 mark· Mathematics Q11 11(a)(ii)State ONE geometrical relationship between BA and BC.
14. 11(a)(iii)2 marks· Mathematics Q11 11(a)(iii)Express OS in terms of u and v.
15. 11(b)(ii)b)1 mark· Mathematics Q11 11(b)(ii)b)Show that P, R and S are collinear.
16. 11(b)(iii)2 marks· Mathematics Q11 11(b)(iii)Using the results of combining the vectors in (b) (ii) on page 33, justify that RS is parallel to ST and that RST is a straight line.
17. 11(b)(iii)2 marks· Mathematics Q11 11(b)(iii)Using your findings in (b)(ii), deduce TWO geometrical relationships between KL and MN.
18. 11(b)(iv)3 marks· Mathematics Q11 11(b)(iv)On the graph provided on page 33, draw the vector OS = [7, 4]. Show that PQRS is a parallelogram.
19. 11(b)(v)4 marks· Mathematics Q11 11(b)(v)Given that OT = (2 5), prove that OSTR is a parallelogram.
20. 11(c)(ii)3 marks· Mathematics Q11 11(c)(ii)R is the mid-point of VW. Prove that R, S and X are collinear.
21. 11(c)(iii)3 marks· Mathematics Q11 11(c)(iii)Given that OP = RQ, determine the coordinates of the point, R.
22. 11(c)(iv)2 marks· Mathematics Q11 11(c)(iv)State the type of quadrilateral formed by PQRO. Justify your answer.
23. 11(c)(iv)2 marks· Mathematics Q11 11(c)(iv)State TWO geometrical relationships between PQ and RS.
24. 13(a)(i)1 mark· Mathematics Q13 13(a)(i)Copy and complete the diagram to show the point B such that OABC is a parallelogram
25. 13(a)(iii)2 marks· Mathematics Q13 13(a)(iii)Hence show that vector PQ = 1/2 vector AC.
26. 13(b)(ii)1 mark· Mathematics Q13 13(b)(ii)Using a vector method, show that OP is parallel to QR.
27. 13(b)(ii)2 marks· Mathematics Q13 13(b)(ii)State TWO geometrical relationships between DX and DC.
28. 13(b)(ii)a)5 marks· Mathematics Q13 13(b)(ii)a)Use a vector method to determine the position vector of F.
29. 13(b)(iii)3 marks· Mathematics Q13 13(b)(iii)Hence, prove that O, G, and H lie on a straight line.
30. 13(b)(iii)1 mark· Mathematics Q13 13(b)(iii)State ONE geometrical relationship between the points D, C, and X.
31. 13(b)(v)3 marks· Mathematics Q13 13(b)(v)Determine the value of k for which MG = CO.
32. 13(c)4 marks· Mathematics Q13 13(c)Use a vector method to prove that P, M and N are collinear.
33. 13(c)4 marks· Mathematics Q13 13(c)Prove that A, P and E are collinear.
34. 13(c)5 marks· Mathematics Q13 13(c)Show by a vector method that triangle ABC is an isosceles triangle.
35. 13(c)4 marks· Mathematics Q13 13(c)Show that PN = 2PM + OP.
36. 13(c)5 marks· Mathematics Q13 13(c)L is the mid-point of RM. Using a vector method, prove that RS is parallel to KL.
37. 13(c)(i)4 marks· Mathematics Q13 13(c)(i)State two geometrical relationships between the line segments OA and CB.
38. 13(c)(i)2 marks· Mathematics Q13 13(c)(i)Using the answers in (a) (ii), state TWO geometrical relationships between the line segments AB and DC.
39. 13(c)(i)3 marks· Mathematics Q13 13(c)(i)determine the coordinates of G
40. 13(c)(ii)4 marks· Mathematics Q13 13(c)(ii)Explain why OABC is a parallelogram.
41. 13(c)(ii)2 marks· Mathematics Q13 13(c)(ii)Explain why ABCD is a parallelogram.
42. 13(c)(ii)5 marks· Mathematics Q13 13(c)(ii)prove, using a vector method, that A, G, and C lie on a straight line.
43. 13(c)(iii)3 marks· Mathematics Q13 13(c)(iii)Using a vector method, show that OPSQ is a parallelogram.
44. 13(d)5 marks· Mathematics Q13 13(d)Using a vector method, determine the position vector of G, the midpoint of the line AC. Hence, state the coordinates of the point of intersection of the diagonals AC and BD of parallelogram ABCD.
45. 13(d)4 marks· Mathematics Q13 13(d)Determine the position vector of the point D, such that BD is parallel to AC and ABDC forms a parallelogram.
46. 13(d)4 marks· Mathematics Q13 13(d)Use a vector method to prove that triangle AED is isosceles.
47. 13(d)5 marks· Mathematics Q13 13(d)Using a vector method, prove that the points A, B and D are collinear.
48. 13(d)(ii)7 marks· Mathematics Q13 13(d)(ii)Determine the position vector ON. Hence, state one conclusion which can be made about the diagonals of the parallelogram OABC.
49. 13(iii)3 marks· Mathematics Q13 13(iii)Show that BC is parallel to DE and is twice the length of DE.