b i ii c + + a b c + 2c d a b e 2(a b) + c f + a b 94 Find the vector in the direction of vector = + 2j 2k such that 5. b a i b= 95 In triangle = 6i + and = 3i 2j. If is the midpoint of find . OAB, j M AB, 96 is a cuboid. = 4j, = 2i and = 2k. OABCDEFG Express the following vectors in terms of and i, j k. a b c d e f g h Analysis is a regular hexagon. 18 ABCDEF a Find the diagonal in terms of and a b. BF b i Find in terms of and AC a b. ii find in terms of and BC a b. Draw a diagonal vector equal to 2b. c v a + d Draw a diagonal vector to 2a 2b. w + 19 and are the midpoints of and respectively. Let = p, W, T, R V SP, PQ, QX SX and = x. a Find in terms of and p r. b Find in terms of and p, r x. c Find in terms of and p, r x. d Find in terms of and p r. e What conclusion can you reach about the quadrilateral Give WTRV? reason(s) for your answer. 20 a The position vectors of and relative to an origin are + A, B C O –i pj, 5i + 9j and 6i + 8j respectively. i Determine the of for which and are collinear. p A, B C ii Given that is a point on such that is a unit vector, find the D OC position vector of relative to D O. b
b i ii c a + b + c d a b + 2c e 2(a b) + c f a + b 94 Find the vector b in the direction of vector a = i + 2j 2k such that b= 5. 95 In triangle OAB, = 6i + j and = 3i 2j. If M is the midpoint of AB, find . 96 OABCDEFG is a cuboid. = 4j, = 2i and = 2k. Express the following vectors in terms of i, j and k. a b c d e f g h Analysis 18 ABCDEF is a regular hexagon. a Find the diagonal BF in terms of a and b. b i Find AC in terms of a and b. ii find BC in terms of a and b. c Draw a diagonal vector v equal to a + 2b. d Draw a diagonal vector w to 2a + 2b. 19 W, T, R and V are the midpoints of SP, PQ, QX and SX respectively. Let = p, and = x. a Find in terms of p and r. b Find in terms of p, r and x. c Find in terms of p, r and x. d Find in terms of p and r. e What conclusion can you reach about the quadrilateral WTRV? Give reason(s) for your answer. 20 a The position vectors of A, B and C relative to an origin O are –i + pj, 5i + 9j and 6i + 8j respectively. i Determine the of p for which A, B and C are collinear. ii Given that D is a point on OC such that is a unit vector, find the position vector of D relative to O. b
VECTORS-REVISION.docx