4 B1 2 B1 cao H 86 a i b a – ii B1 B1 cao –2a iii 2b a B1 B1 cao – 2b B1 B1 cao iv a – b B1 B1 for parallel Parallel and equal in length. B1 B1 for equal in length 6 87 a They lie in a straight line, C1 2 C1 for clearly stating they lie in a straight line H AC = × C1 C1 for explaining one is a multiple of the other b = – M1 M1 for finding 9a + 6b (6a + 4b) – A1 A1 forcao = 3a + 2b is 2 × So AB : BC = 2 : 1 B1 for correct ratio B1 5 88 a i = c b B1 2 B1 cao H – 3 ii = b + (c b) M1 M1 method of finding NQ – = c A1 A1 cao = a + AC iii = c a M1 M1 method of finding MP – = a + (c a) B1 B1 cao – = c It is a parallelogram, because A1 A1 cao = = c and hence they are parallel and equal in B1 B1 for parallelogram b length. C2 C1 for stating vectors are parallel C1 for stating vectors will be same length 9
4 86 a i ii iii iv b b – a –2a 2b – a 2b – a Parallel and equal in length. B1 B1 B1 B1 B1 B1 2 B1 cao B1 cao B1 cao B1 cao B1 for parallel B1 for equal in length H 6 87 a b They lie in a straight line, AC = × = – 9a + 6b – (6a + 4b) = 3a + 2b is 2 × So AB : BC = 2 : 1 C1 C1 M1 A1 B1 2 C1 for clearly stating they lie in a straight line C1 for explaining one is a multiple of the other M1 for finding A1 forcao B1 for correct ratio H 5 88 a i ii iii b = c – b = b + (c – b) = c = a + AC = c – a = a + (c – a) = c It is a parallelogram, because = = c and hence they are parallel and equal in length. B1 M1 A1 M1 B1 A1 B1 C2 2 3 B1 cao M1 method of finding NQ A1 cao M1 method of finding MP B1 cao A1 cao B1 for parallelogram C1 for stating vectors are parallel C1 for stating vectors will be same length H 9