Mathematics Higher Level Robert Joinson

©Sumbooks2002Higher Level39. Vectors 11. In the quadrilateral, AB , BC,and CD arerepresented by the vectors b, c, and d. Find, interms of b, c, and d AC , AD, and BD2. AB = ⎛2⎞and BC = ⎛3⎞⎝3⎠⎝5⎠calculate AC inbracket form.3. Express AB + BC + CD in its simplest form.4. OABC is a parallelogram. If OA = 4a andAbABcCdDBOC = 4c. Find, in terms of a and c (a) AC 4a(b) AP where P is the mid point of AC(c) OP (d) If X is the mid point of CB find O4cCPX . (e) What is the geometrical relationshipbetween PX and OC ?15. In triangle OAB, OA = 6a and OB = 9b. Point P is on AB such that AP = --PB. Find, in2terms of a and b (a) AB (b) AP (c) OP.6. OABC is a triangle with point C half way along OB. OA = aAandAB= b. Find, in terms of a and bab(a) OB (b) OC (c) AC7. ABCDEF is a regular hexagon with centre O . OA = a andOB = b . Express in terms of a and b the vectorsOD, OE, DA, BC, OC and CF .OEFC. OABB8. (a) If AB = 3a and CD = 6a write down the geometricalrelationship between AB and CD.D C(b) What is the geometrical relationship between vectors 4a + 2b and 6a + 3b?9. OAB is a triangle with point X half way along OA and YOhalf way along OB. If OA = 2a and OB = 2b. Find, interms of a and b, (a) AB (b) XY and (c) show that XYis parallel to AB.10. In a rectangle ABCD, AB = a and BC = b. Find, in Aterms of a and b the vectors AC and BD.X. .YB