Points and have position vectors and respectively, relative to the p q P Q The point on is such that = The point on is O. R OP OR OP. S RQ such that = RS RQ. Express and in terms of and i p q. produced meets at where = PS OQ T, OT  OQ. ii Express in of and and evaluate ,  p q, 21 The position of a boat at point is given by the vector = 2i The position of B j. – a light house at is given by = 3i + (Distances are measured in kilometres.) j. A a i Find . ii Find ||. iii If is a unit vector in the east direction and a unit vector in the i j north direction, find the bearing of from B A. b The boat now moves at a speed of 4 km/h in an easterly direction. Find its position relative to after O i 3 hours ii hours t c Find the distance of the boat from the lighthouse after hours. t ANSWERS: MC: 91 D 92 D C 93 94 D 95 C 96 B 97 A D 98 99 E 100 C SA: 90 a b (–3i 5k) j – 91 a i + = 3i + a b j ii = 7j a b i iii = (2i 3j) 92 a = (i + k) = + b a b c = = 93 a i ii 3 b i (i + j) (i + 2j 2k) ii c 4i + 2j 2k d + 6j 4k i e + 6j 2k i
Points P and Q have position vectors p and q respectively, relative to the O. The point R on OP is such that OR = OP. The point S on RQ is such that RS = RQ. i Express and in terms of p and q. PS produced meets OQ at T, where OT =  OQ. ii Express in of , p and q, and evaluate  21 The position of a boat at point B is given by the vector = 2i – j. The position of a light house at A is given by = 3i + j. (Distances are measured in kilometres.) a i Find . ii Find ||. iii If i is a unit vector in the east direction and j a unit vector in the north direction, find the bearing of B from A. b The boat now moves at a speed of 4 km/h in an easterly direction. Find its position relative to O after i 3 hours ii t hours c Find the distance of the boat from the lighthouse after t hours. ANSWERS: MC: 91 D 92 D 93 C 94 D 95 C 96 B 97 A 98 D 99 E 100 C SA: 90 a b (–3i j – 5k) 91 a i a + b = 3i + j ii a b = i 7j iii = (2i 3j) 92 a = (i + k) b = a + b c = = 93 a i ii 3 b i (i + j) ii (i + 2j 2k) c 4i + 2j 2k d i + 6j 4k e i + 6j 2k
VECTORS-REVISION.docx