MENU
Educational Resources
Exam Papers
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 3 Mathematics: Vectors II Questions and Answers
Given that P=2i-3j+k, Q=3i-4j-3k and R=3P+2Q, find the magnitude of R to 2 significant figures.
(3m 20s)
2407 Views
SHARE
|
« Previous
Next »
1.
In a parallelogram ABCD, AB=2a and AD=b. M is the midpoint of AB. AC cuts MD at X. (i) Express AC in terms of a and b. (ii) Given that AX=mAC and MX=nMD, where m and n are constants, find m and n.
2.
In the figure below, E is the midpoint of BC, AD:DC=3:2 and F is the point of intersection of BD and AE. (i) Given that AB=b and AC=c, express AE and BD in terms of b and c. (ii) Given further that BF=tBD and AF=sAE, find the values of s and t.
3.
Three points A, B and P are in straight line such that AP=tAB. Given that the coordinates of A, B and P are (3, 4), (8, 7) and (x, y) respectively, express x and y in terms of t.
4.
The vectors p, q and y are expressed in terms of the vectors t and s as follows: p= 3t + 2s q= 5t – s y=ht + (h-k)s Where h and k are constants. Given that y=2p-3q, find the values of h and k.
5.
Find the position vector of point R which divides line MN internally in the ratio 2:3. Take the position vectors of M and N to be
6.
In the diagram below, OABC is a parallelogram, OA=a and AB=b. N is a point on OA such that ON:NA = 1:2. (a) Find: (i) AC in terms of a and b. (ii) BN in terms of a and b. (b) The lines AC and BN intersect at X, AX=hAC and BX=kBN. (i) By expressing OX in two ways, find the values of h and k. (ii) Express OX in terms of a and b.
7.
The points P, Q and R lie on a straight line. The position vectors of P and R are 2i + 3j + 13k and 5i – 3j + 4k respectively. Q divides PR internally in the ratio 2:1. Find the (a) Position vector of Q. (b) Distance of Q from the origin.
8.
The figure below shows triangle OAB in which M divides OA in the ratio 2:3 and N divides OB in the ratio 4:1. AN and BM intersect at X. (a) Given that OA=a and OB=b, express in terms of a and b: (i) AN (ii) BM (b) 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 values of s. hence write OX in terms of a and b.
9.
The position vectors for points P and Q are 4i + 3j + 2k and 3i – 6j + 6k respectively. Express vector PQ in terms of unit vectors i, j and k. Hence find the length of PQ, leaving your answer in simplified surd form.
10.
The figure below shows a parallelogram OPQR with O as the origin, OP=P and OR=r. Point T divides RQ in the ratio 1:4. PT meets OQ as S. (a) Express in terms of p and r, the vectors (i) OQ (ii) OT (b) Vector OS can be expressed in two ways: mOQ or OT + nTP, where m and n are constants. Express OS in terms of (i) m, p and r. (ii) n, p and r. Hence find the: (iii) Value of m. (iv) Ratio OS:SQ
11.
The position vectors of points X and Y are x=2i+j-3k and y=3i+2j-2k respectively. Find XY.
12.
Given that x=2i+j-2k, y=-3i+4j-k and z=-5i+3j+2k and that p=3x-y+2z, find the magnitude of vector p to 3 significant figures.
13.
In the figure below, OP=p and OR=r. Vector OS=2r and OQ= #3/2#p. (a) Express in terms of p and r: (i) QR (ii) PS (b) The lines QR and PS intersect at K such that QK=mQR and PK=nPS, where m and n are scalars. Find two distinct expressions for OK in terms of p, r, m and n. Hence find the values of m and n. (c) State the ratio PK:KS.
14.
Given that OA=3i-2j+k and OB=4i+j-3k. Find the distance between points A and B to 2 decimal places.
15.
Point T is the midpoint of a straight line AB. Given that the position vectors of A and T are i-j+k and 2i+1 #1/2# k respectively, find the position vector of B in terms of i, j and k.
16.
Given that qi+ #1/3#j+#2/3# k is a unit vector, find q.
17.
In the figure below, OQ=q and OR=r. point X divides OQ in the ratio 1:2 and Y divides OR in the ratio 3:4. Lines XR and YQ intersect at E. (a) Express in terms of q and r. (i) XR (ii) YQ (b) If XE=mXR and YE=nYQ, express OE in terms of (i) r, q and m. (ii) r, q and n. (c) Using the results in (b) above, find the values of m and n.
18.
Vector q has a magnitude of 7 and is parallel to vector p. given that p=3i-j+1 #1/2# k, express vector q in terms of i, j and k.
19.
In the figure below, AB=p, AD=q, DE= #1/2#AB and BC= #2/3#BD. (a) Find in terms of p and q, the vectors: (i) BD (ii) BC (iii) CD (iv) AC (b) Given that AC=kCE, where k is a scaler, find: (i) The value of k. (ii) The ratio in which C divides AE.
20.
The position vectors of points A and B are #((3),(-1),(-4))# and #((8),(-6),(6))# respectively. A point P divides AB in the ratio 2:3. Find the position vector of point P.
21.
In the figure below, ABCD is a trapezium. AB is parallel to DC, diagonals AC and DB intersect at X and DC=2AB. AB=a, DA=d, AX=kAC and DX=hDB, where h and k are constants. (a) Find in terms of a and d: (i) BC (ii) AX (iii) DX (b) Determine the values of h and k.
22.
Given that P=2i-3j+k, Q=3i-4j-3k and R=3P+2Q, find the magnitude of R to 2 significant figures.
23.
In triangle OPQ below, OP=p, OQ=q. Point M lies on OP such that OM:MP=2:3 and point N lies on OQ such that ON:NQ=5:1. Line PN intersects line MQ at X. (a) Express in terms of p and q: (i) PN (ii) QM (b) Given that PX=kPN and QX=rQM, where k and r are scalers: (i) Write two different expressions for OX in terms of p, q, k and r. (ii) Find the values of k and r. (iii) Determine the ratio in which X
24.
In the figure below, OABC is trapezium. AB is parallel to OC and OC=5AB. D is a point on OC such that OD:DC=3:2. (a) Given that OA=p and AB=q, express in terms of p and q: (i) OB (ii) AD (iii) CB (b) Lines OB and AD intersect at point X such that AX=kAD and OX=rOB, where k and r are scalars. Determine the values of k and r.
25.
The position vectors of points F, G and H are f, g and h respectively. Point H divides FG in the ration 4:-1. Express h in terms of f and g.
26.
Vectors r and s are such that r=7i+2j-k and s=-i+j-k. Find|r+s |.
27.
In the figure below, OA=a and OB=b. M is the mid-point of OA and AN:NB=2:1. (a) Express in terms of a and b: (i) BA (ii) BN (iii) ON (b) Given that BX=hBM and OX=kON, determine the values of h and k.
×
Share Content Via:
Facebook
Twitter
WhatsApp
Close
Get premium membership