MENU
Educational Resources
Form 1 Videos
Form 2 Videos
Form 3 Videos
Form 4 Videos
Grade 4 Videos
Grade 5 Videos
Grade 6 Videos
Grade 7 Videos
Class 8 Videos
Form 1 Exams
Form 2 Exams
Form 3 Exams
Form 4 Exams
KCSE Videos
Class 8 Exams
Grade 5 Exams
Grade 4 Exams
Grade 3 Exams
Grade 2 Exams
Grade 1 Exams
Online Tests
Online Tuition
Sign In
Join
Get access to thousands of educational resources
Get premium membership
and access revision papers with marking schemes, video lessons and live classes.
OR
Processing. Please wait.
Form 2 Mathematics Vectors I Questions and Answers
Find scalars m and n such that #m ((4),(3))+n((-2),(1))= ((0),(-3))#
(2m 14s)
764 Views
SHARE
|
« Previous
Next »
1.
In the figure beside, AB=p, AC=q, AD=#3/5# AC and CE=#2/3# CB. Express DE in terms of p and q.
2.
In a triangle ABC, D is the midpoint of AB and E is a point on BC such that BE=#2/3# BC. If AD=p and AC=q, express EC in terms of p and q.
3.
A point T divides a line AB internally in the ratio 5:2. Given that A is (-4, 10) and B is (10, 3), find the coordinates of T.
4.
OABC is a trapezium such that the coordinates of O, A, B and C are (0,0), (2,-1), (4,3) and (0,y). (a) Find the value of y (b) M is a midpoint if AB and N is a midpoint of OM. Show that A,N and C are collinear.
5.
OABC is a trapezium in which OA=a, OC=c and CB=3a. CB is produced to D such that CB:BD=3:1. E is a point on AB such that AB=2AE. Show that O, E and D are collinear.
6.
In the figure below CA=b, CB=a, AX=XY and AY=YB. Express CX in terms of a and b.
7.
In the figure below OC=3CA and OD =3DB. By taking OA=a, OB=b show that CD//AB.
8.
In the figure below, ABCD is a parallelogram. AOC and BOD are diagonals of the parallelogram. Show that the diagonals of the parallelogram bisect each other. Give reasons.
9.
The figure below is a right pyramid with a rectangular base ABCD and VO as the height. The vectors AD=a, AB=b and DV=c (a) Express (i) AV in terms of A and c (ii) BV in terms of a, b and c (b) M is a point on OV such that OM: MV=3:4. Express BM in terms of a, b and c. Simplify your answer as far as possible.
10.
In the figure below, OA=3i+4j and OB=8i-j. C is a point on AB such that AC:CB=3:2, and D is a point such that OB//CD and 2OB=CD Determine the vector DA in terms of i and j
11.
ABC is triangle and P is a point on AB such that p divides AB internally in the ratio 4:3. Q is a point on AC such that PQ is parallel to BC. If AC=14cm, (i) State the ratio AQ:QC (ii) Calculate the length of QC
12.
In the figure below, KLMN is a trapezium in which KL is parallel to NM and KL=3NM Given that KN=w, NM=u and ML=v, show that 2u=v+w
13.
In triangle OAB, #vec ( OA)#=a, #vec (OB)#=b and P lies on AB such that AP: PB=3:5 (a) Find in terms of a and b the vectors (i) #vec (AB)# (ii) #vec (AP)# (iii) #vec (BP)# (iv) #vec (OP)# (b) Point Q is on OP such that #AQ= -5/8 a+ 9/40 b#. Find the ratio OQ:QP
14.
The coordinates of points O, P, Q and R are (0, 0), (3, 4), (11, 6) and (8, 2) respectively. A point T is such that vectors OT, QP and QR satisfy the vector equation #OT=QP+ 1/2QR# Find the coordinates of T.
15.
(a) If A, B and C are the points (2, -4), (4,0) and (1,6) respectively, use the vector method to find the coordinates of the points D given that ABCD is a parallelogram. (b) The position vectors of points P and Q are p and q respectively. R is another point with position vector, #r=3/2 q- 1/2 p#. Express in terms of p and q (i) PR (ii) RQ, hence show that P, Q and R are collinear.
16.
The points P,Q, R and S have position vectors 2p, 3p,r and 3r respectively, relative to an origin O. A point T divides PS internally in the ratio 1:6. (a) Find in the simplest form the vectors OT and QT in terms of p and r (b) (i) Show that the point Q,T and R lie on a straight line (ii) Determine the ratio in which T divides QR
17.
Two points P and Q have coordinates (-2, 3) and (1, 3) respectively. A translation maps point P to P’ (10, 10). (a) Find the coordinates of Q’, the image of Q under the translation. (b) The position vectors of P and Q in (a) above are p and q respectively. Given that mp-nq=#((-12), (9))#, find the values of m and n
18.
In the diagram below, the coordinates of points A and B are (1, 6) and (15, 6) respectively. Point N is on OB such that 3ON=2OB. Line OA is produced to L such that OL= 3OA. (a) Find vector LN (b) Given that a point M is on LN such that LM:MN=3:4, find the coordinates if M . (c) If line OM is produced to T such that OM:MT=6:1 (i) Find the position vectors of T (ii) Show that points L, T and B
19.
The position vectors of points A and B with respect to the origin O are #((-8),(5 ))# and #((12),(-5))# respectively. Point M is the midpoint of AB and N is the midpoint of OA. (a) Find: (i) the coordinates of N and M (ii) the magnitude of NM (b) Express vector NM in terms of OB (c) Point P maps onto P’ by a translation #((-5),(8))#. Given that OP=OM+2MN, find the coordinates of P’.
20.
Vector OA=#((2),(1)) # and OB=#((6),(-3))#. Point C is on OB such that CB=2OC and point D is on AB such that AD =3DB. Express CD as a column vector.
21.
In the figure below, OPQR is a trapezium in which PQ is parallel to OR and M is the midpoint of QR, OP=p, OR=r and #PQ=1/3 OR#. Find OM in terms of p and r
22.
Vectors OP=6i+j and OQ=-2i+5j. A point N divides PQ internally in the ratio 3:1. Find PN in terms of i and j
23.
Given that OA=2i+3j and OB= 3i -2j. Find the magnitude of AB to one decimal place.
24.
Given that p=5a-2b where a=#((3),(2))# and b=#((4),(1))#. Find (a) Column vector p; (b) P’, the image of P under translation vector#((-6),(4 ))#.
25.
The position vectors of point P, Q and R are OP=#((-3),(6))#, OQ=#((2),(1))# , OR=#((4),(-1))# . Show that P, Q and R are collinear.
26.
Given that a= #((4),(3))#, c=#((-2),(-5))# and 3a-2b+4c=#((10),(-19))# , find b
27.
Given that OA=3i+4j+7k, OB=4i+3j+9k and OC=i+6j+3k, show that points A, B and C are collinear.
28.
Given that OA=#((2),(3))# and OB=#((-4),(5))# . Find the midpoint M of AB
29.
Given that b=#((2),(4))# , c=#((3),(2))# and a=3c-2b, find the magnitude of a, correct to 2 decimal places.
30.
Given that t = 2a - b and r = b + 3a, find, in terms of a and b, the following vectors: (a) 2t - 2r (b) –t + #1/2#r (c) 2r – t
31.
Simplify: (a) 3(a – 2b) – 4(5a – b) (b) #1/3#(a - b) + #1/4#(3b - 4a) (c) 3a – 2b – c + 4(#1/2# a- #3/2# c) + #1/3#(6a –9b)
32.
If #1/3# a- #1/5# b = 0, write a as a multiple of b.
33.
If a =#((3),(1))#, b =#((-2),(7))#, c = #((6),(5))# and d=#((0),(-5))#, find: (a) 3a - 2b (b) #1/3#a + #1/3b# + #1/3#c (c) 10a+15b+23d (d) The scalars r and s such that ra + sc = 9b
34.
If x = #((-1),(0))# and z=#((3),(-1))#, find –y, given that x + y = z.
35.
Find the co-ordinates of P if OP = OA + OB – OC and the co-ordinates of points A, B, C are (3, 4), (-3, 4) and (-3, -4) respectively.
36.
In the figure below, OAB is a triangle. A is the point (2, 8) and B the point (10, 2). C, D, and E are midpoints of OA, OB and AB respectively. (a) Find the co-ordinates of C and D. (b) Find the length of the vectors CD and AB.
37.
Find the co-ordinates of the midpoint of AB in each of the following cases: (a) A (-4, 3), B (2, 0) (b) A (0, 0), B (a, b)
38.
Triangle OAB is such that OA = a and OB = b. C lies on OB such that OC: CB = 1:1. D lies on AB such that AD: DB=1:1 and E lies on OA such that OA: AE = 3:1. Find: (a) OC (b) OD (c) OE (d) CD (e) DE
39.
The co-ordinates of A, B, C and D are (-2, 5), (1, 3), (3, -2) and (2, -4) respectively. If A' is (-5, 6) under a translation T, find the co-ordinates of B', C' and D' under T.
40.
A point P (-2, 3) is given the translation#((-1),(4))#. Find the point P', the image of P, under the translation. If P' is given a translation#((1),(-2))#, find the co-ordinates of P", the image of P'. Find a single translation that maps P onto P".
41.
The point A (3, 2) maps onto A' (7, 1) under a translation T_1. Find#T_1#. If A' is mapped onto A" under translation #T_2# given by#((-3),(5))#, find the co-ordinates of A". Given that #T_3 (A)# = A", find #T_3#.
42.
The image of point (6, 4) is (3, 4) under a translation. Find the translation vector.
43.
Draw #triangle# PQR with vertices P (3, 2), Q (5, 0) and R (4, -1). On the same axes, plot P'Q'R', the image of #triangle# PQR under a translation given by #((-4),(1))#.
44.
The figure below shows ABC a triangle in which the midpoints of AB, BC and AC are E, F and D respectively. Vector AB = -2b while BC = 2a. Rewrite each of the following vectors in terms of a and b: (a) BF (b) AF (c) AC (d) DC (e) DA (f) BD
45.
Given that t = 2a - b and r = b + 3a, find, in terms of a and b, the following vectors: (a) 2t (b) #1/2# r (c) -t (d) -2r
46.
The figure below shows a regular hexagon PQRSTU. PQ = a, QR = b and RS = c. Write in terms of a, b and c each of the following: (a) QP (b) PS (c) TQ (d) TP (e) RT (f) UQ (g) US
47.
Simplify: a) #3a + 2b - c + 4 (1/2a-3/2c) + 1/3(6a-9b)# (b) 2u - 3v + 2(w - u) + 3(u + v) (c) (p - q) + (r - p) + (q - r)
48.
If #a=((3),(1)), b=((-2),(7)), c=((6),(5)) and d=((0),(-5))#, find: (a) 5b-3a (b) #1/2c-3/2d# (c) 3b+c
49.
Find scalars m and n such that #m ((4),(3))+n((-2),(1))= ((0),(-3))#
50.
Find the co-ordinates of the midpoint of AB in each of the following cases: (a) A (0, 4), B (0, -2) (b) A (-3, 2), B (4, 2)
51.
For each of the points below, give the image when it is translated by the given vector: (a) #(2, 3); ((4),(3))# (b) #(0, 0); ((-2),(1))# (c) #(-2,-4); ((4),(3))#
52.
For each of the points below, give the image when it is translated by the given vector: (a) #(-4, 3); ((4),(-3))# (b) #(7, 0); ((-8),(-1))# (c) #(8, -2); ((-10),(4))#
53.
Below are images of points which have been translated by the vectors indicated; Find the corresponding object points: (a) #(2, 3); ((1),(1))# (b) #(0, 0); ((4),(3))# (c) #(9, 17); ((2),(3))#
54.
Below are images of points which have been translated by the vectors indicated; Find the corresponding object points: (a) #(5, 6); ((-2),(-4))# (b) #(7,-2); ((-5),(2))# (c) #(-2, 4); ((7),(5))#
55.
Below are images of points which have been translated by the vectors indicated; Find the corresponding object points: (a) #(3, 3); ((-4),(-10))# (b) #(-5,-11); ((-12),(-0))# (c) #(4, 3); ((0),(0))# (d) #(a, b); ((c),(d))#
×
Share Content Via:
Facebook
Twitter
WhatsApp
Close
Get premium membership