Questions
 If OA = 12i + 8j and OB = 16i + 4j. Find the coordinates of the point which divides AB
internally in the ratio 1:3  Find scalars m and n such that
m(^{4}_{3}) + n(^{3}_{2}) = (^{5}_{8})  In a triangle OAB, M and N are points on OA and OB respectively, such that OM: MA = 2:3 and ON: NB = 2:1. AN and BM intersect at X. Given that OA = a and OB = b.
 Express in terms of a and b
 BM
 AN
 By taking BX = t and AX = hAN, where t and h are scalars, express OX in two different ways
 Find the values of the scalars t and h
 Determine the ratios in which X divides :
 BM
 AN
 Express in terms of a and b
 OABC is a parallelogram, M is the midpoint of OA and AX = ^{2}/_{7}AC, OA=a and OC = c.
 Express the following in terms of a and c
 MA
 AB
 AC
 AX
 Using triangle MAX, express MX in terms of a and c
 The coordinates of A and B are (1, 6, 8) and (3, 0, 4) respectively. If O is the origin and P the midpoint of AB. Find;
 Length of OP
 How far are the midpoints of OA and OB?
 Express the following in terms of a and c

 If A, B & C are the points (2,  4), (4, 0) and (1, 6) respectively, use the vector method to find the coordinates of point D given that ABCD is a parallelogram.
 The position vectors of points P and Q are p and q respectively. R is another point with position vector r = ^{3}/_{2}q  ½p. Express in terms of p and q
 PR
 PQ, hence show that P, Q & R are collinear.
 Determine the ratio PQ : QR
 The figure shows a triangle of vectors in which OS: SP = 1:3, PR:RQ = 2:1 and T is the midpoint of OR.
 Given that OP = p and OQ = q, express the following vectors in terms of P and q
 OR
 QT
 Express TS in terms of p and q and hence show that the points Q, T and S are collinear.
 M is a point on OQ such that OM = KOQ and PTM is a straight line. Given that
PT: TM = 5:1, find the value of k
 Given that OP = p and OQ = q, express the following vectors in terms of P and q
 Given that a = (^{3}_{2}), b = (^{4}_{6}) and c = (^{5}_{10}) and that p = 3a – ½b +^{1}/_{10}c
Express p as a column vector and hence calculate its magnitude /P/ correct to two decimal places  In a triangle OAB, M and N are points on OA and OB respectively, such that OM:MA= 2:3 and ON:NB= 2:1. AN and BM intersect at X. Given that OA = a and OB = b
 Express in terms of a and b:
 BM
 AN
 Taking BX = kBM and AX =hAN where k and h are constants express OX in terms of
 a, b and k only
 a, b, and h only
 Use the expressions in (b) above to find values of k and h
 Express in terms of a and b:
 In the figure below OAB is a triangle in which M divides OA in the ratio 2:3 and N divides OB in the ratio 4:1. AN and BM intersects at X.
 Given that OA = a and OB = b, express in terms of a and b
 AN
 BM
 AB
 If AX = sAN and BX = tBM, where s and t are constants, write two expressions for OX in terms of a, b, s and t. Find the value of s and t hence write OX in terms of a and b
 Given that OA = a and OB = b, express in terms of a and b
 Given that: r = 5i – 2j and m = 2i + 6j – k are the position vectors for R and M respectively. Find the length of vector RM.
 OABC is a trapezium in which OA = a and AB = b. AB is parallel to OC with 2AB = OC.
T is a point on OC produced so that OC: CT = 2:1. AT and BC intersect at X so that BX = hBC and AX = KAT Express the following in terms of a and b:
 OB
 BC
 Express CX in terms of a, b and h
 Express CX in terms of a, b and k
 Hence calculate the values of h and k
 Express the following in terms of a and b:
 Given that a = 2i + j – 2k and b = 3i + 4j – k find :
 a + b.  In the figure below, E is the midpoint of BC. AD:DC=3:2 and F is the meeting point of
BD and AE. If AB = b and AC = c; Express BD and AE in terms of b and c
 If BF =tBD and AF =nAE, find the values of t and n
 State the ratios in which F divides BD and AE
 The coordinates of point O, A, B and C are (0, 0) (3, 4) (11, 6) and (8, 2) respectively.
A point P is such that the vector OP, BA, BC satisfy the vector equation OP = BA + ½ BC. Find the coordinates of P.  A point Q divides AB in the ratio 7:2. Given that A is (3, 4) and B(2, 1).
Find the coordinates of Q
Answers
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