Category: Vectors II

QUESTION AND ANSWER ON VECTORS II MODEL06012023003

5/1/2023

Comments

QUESTION AND ANSWER ON VECTORS II MODEL06012023017

5/1/2023

Comments

Given that, the coordinates of two points P and Q are (■(2,&3,&5)) and (■(6,&k-1,&15)) respectively and that their position vectors are parallel, Calculate the value of |PQ|. (4marks)

11/12/2022

Comments

The diagram below shows a triangle OPQ in which M and N are points on OQ and PQ respectively such that OM = ⅔ OQ and PN = 1/4 PQ. Lines PM and ON meets at X.

30/11/2021

Comments

VECTORS (2) | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION B

The diagram below shows a triangle OPQ in which M and N are points on OQ and PQ respectively such that OM = ⅔ OQ and PN = ¼ PQ. Lines PM and ON meets at X.

(a) Given that OP = P and OQ = q express in term of P and q the vectors.
(i) PQ

PQ=q-p

(ii) PM. (2mks)

(iii) ON. (2mks)

(b) You are further given that OX = KON and PX = hPM.
(i) Express OX in terms of P and q in two different ways. (2mks)

(ii) Find the value of h and K. (2mks)

(iii) Find the ratio PX : XM. (1mk)

Comments

The diagram below shows a square based pyramid V vertically above the middle of the base. PQ = 10cm and VR = 13cm. M is the midpoint of VR.

29/11/2021

Comments

VECTORS II | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION B

The diagram below shows a square based pyramid V vertically above the middle of the base. PQ = 10cm and VR = 13cm. M is the midpoint of VR.

Find
(a) (i) the length of vector PR. (2mks)

(ii) The height of the pyramid. (2mks)

(b) (i) the angle between VR and the base PQRS. (2mks)

(ii) The angle between MR and the base PQRS. (2mks)

(iii) The angle between the planes QVR and PQRS. (2mks)

Comments

Given that position vectors of points A and B are

19/11/2021

Comments

Worked Solution

Comments

K.C.S.E Mathematics Q & A - MODEL 2019PP2QN23

24/9/2020

Comments

Form 3 Mathematics

In the figure below, OA = a, OB = b and BX meets OY at C. OX:OA = 1:2 and BY:YA = 1:3.

(a) Express in terms of a and b:
(ii) OY;
(iii) BX.
(b) Given that OC = hOY and BC = kBX, determine the values of h and k.

answers

Comments

K.C.S.E Mathematics Q & A - MODEL 2019PP2QN13

24/9/2020

Comments

Form 3 Mathematics

answer

Comments

K.C.S.E Mathematics Q & A - MODEL 2019PP1QN11

22/9/2020

Comments

Form 3 Mathematics

answer

Comments

K.C.S.E Mathematics Q & A - MODEL 2018PP2QN13

21/9/2020

Comments

Form 3 Mathematics

In the figure below OP = p, OR = r, PQ:QR = 1:2 and PS = 3PR.

Express QS in terms of p and r.

answer

Comments

K.C.S.E Mathematics Q & A - MODEL 2005.PP1.QN.18

19/9/2020

Comments

Form 3 Mathematics

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 P and r ( 4 marks)
(b)

(i) Show that the points Q, T, and R lie on a straight line ( 3 marks)
(ii) Determine the ratio in which T divides QR ( 1 mark)

Answer

Comments

K.C.S.E Mathematics Q & A - MODEL 2005.PP1.QN.13

17/9/2020

Comments

Form 3 Mathematics

Point T is the midpoint of a straight line AB. Given the position vectors of A and T are i-j + k and 2i+ 1 ½ k respectively, find the position vector of B in terms of i, j \ and k. ( 3 marks)

Answer

Comments

K.C.S.E Mathematics Q & A - MODEL 2017PP2QN16

17/9/2020

Comments

Form 3 Mathematics

Given that OA = 3i+ 4j+ 7k, OB= 4i + 3j + 9k and OC = i + 6j + 3k. show that points A, B and C are collinear.

answer

Comments

K.C.S.E Mathematics Q & A - MODEL 2005.PP1.QN.6

17/9/2020

Comments

Form 3 Mathematics

A point R divides a line PQ internally in the ration 3:4. Another point S, divides the line PR externally in the ration 5:2. Given that PQ = 8cm, calculate the length of RS, correct to 2 decimal places.

Answer

Comments

K.C.S.E Mathematics Q & A - MODEL 2016PP2QN11

15/9/2020

Comments

Form 3 Mathematics

Given that qi + 1/3j + 2/3k is a unit vector, find q.

answer

Comments

K.C.S.E Mathematics Q & A - MODEL 2016PP1QN20

14/9/2020

Comments

Form 3 Mathematics

In the diagram below, the coordinates of points A and B are (1,6) and (15, 6) respectively.

Point N is on OB and that 30N = 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 coordinate of M
c) If line OM is produced to T such a that OM: MT= 6:1
i)Find the position vector of T
ii) Show that points L, T and B are collinear

ANSWERS

Comments

K.C.S.E Mathematics Q & A - MODEL 2016PP1QN05

12/9/2020

Comments

Form 3 Mathematics

Give that OA =2i a + 3 j and OB = 3i -2j, find the magnitude of AB to one decimal place

answer

Comments

K.C.S.E Mathematics Q & A - MODEL 2004.PP1.QN.21

12/9/2020

Comments

Form 3 Mathematics

If A,B and C are the points P and Q are p and q respectively is another point with position vector r = 3q - ½p. Express in terms of p and q.

i) PR
ii) RQ hence show that P,Q and R are collinear.
iii) Determine the ratio PQ:QR.

Answer

Comments

K.C.S.E Mathematics Q & A - MODEL 2015PP2QN16

10/9/2020

Comments

Form 3 Mathematics

answer

Comments

K.C.S.E Mathematics Q & A - MODEL 2004.PP1.QN.4

9/9/2020

Comments

Form 3 Mathematics

Given that OA = 3i - 2j + and OB = 4i + j – 3k. Find the distance between points A and B to 2 decimal places.

Answer

Comments

K.C.S.E Mathematics Q & A - MODEL 2014PP2QN22

8/9/2020

Comments

Form 3 Mathematics

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.

answers

Comments

K.C.S.E Mathematics Q & A - MODEL 2003PP1QN021

4/9/2020

Comments

Form 3 Mathematics

In the figure below, vector OP = P and OR =r. Vector OS = 2r and OQ = ³/₂p.

ANSWER

Comments

K.C.S.E Mathematics Q & A - MODEL 2013PP1QN22

2/9/2020

Comments

Form 3 Mathematics

In the figure below, OABC is a trapezium. AB 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 k and r.

answers

Comments

K.C.S.E Mathematics Q & A - MODEL 2012PP2QN19

1/9/2020

Comments

Form 3 Mathematics

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) PM
(ii) QM.
(c) Given that PX = kPN and QX = rQM, where k and r are scalars:
(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 divides line MQ.

answers

Comments

K.C.S.E Mathematics Q & A - MODEL 2003PP1QN006

1/9/2020

Comments

Form 3 Mathematics

Give 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.

Answer

Comments

<<Previous

KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

Topically Analysed

VECTORS (2) | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION B

​The diagram below shows a triangle OPQ in which M and N are points on OQ and PQ respectively such that OM = ⅔ OQ and PN = ¼ PQ. Lines PM and ON meets at X.

(a) Given that OP = P and OQ = q express in term of P and q the vectors. (i) PQ

​(ii) PM. (2mks)

​(iii) ON. (2mks)

​(b) You are further given that OX = KON and PX = hPM. (i) Express OX in terms of P and q in two different ways. (2mks) (ii) Find the value of h and K. (2mks) (iii) Find the ratio PX : XM. (1mk)

VECTORS II | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION B

The diagram below shows a square based pyramid V vertically above the middle of the base. PQ = 10cm and VR = 13cm. M is the midpoint of VR.

​Find (a) (i) the length of vector PR. (2mks)

​(ii) The height of the pyramid. (2mks)

(b) (i) the angle between VR and the base PQRS. (2mks)

(ii) The angle between MR and the base PQRS. (2mks)

(iii) The angle between the planes QVR and PQRS. (2mks)

Worked Solution

Form 3 Mathematics

23

Form 3 Mathematics

13

Form 3 Mathematics

11

Form 3 Mathematics

13

Form 3 Mathematics

N.18

Form 3 Mathematics

N.13

Form 3 Mathematics

16

Form 3 Mathematics

N.6

Form 3 Mathematics

11

Form 3 Mathematics

20

Form 3 Mathematics

5

Form 3 Mathematics

N.21

Form 3 Mathematics

16

Form 3 Mathematics

N.4

Form 3 Mathematics

22

Form 3 Mathematics

21

Form 3 Mathematics

22

Form 3 Mathematics

19

Form 3 Mathematics

6

Categories

Archives

HIGH SCHOOL EXAMINATIONS

COLLEGE RESOURCES

FREE NOVELS

PRIMARY SCHOOL RESOURCES 8-4-4

PRIMARY SCHOOL RESOURCES CBC

The diagram below shows a triangle OPQ in which M and N are points on OQ and PQ respectively such that OM = ⅔ OQ and PN = ¼ PQ. Lines PM and ON meets at X.

(a) Given that OP = P and OQ = q express in term of P and q the vectors.
(i) PQ

(ii) PM. (2mks)

(iii) ON. (2mks)

(b) You are further given that OX = KON and PX = hPM.
(i) Express OX in terms of P and q in two different ways. (2mks)

(ii) Find the value of h and K. (2mks)

(iii) Find the ratio PX : XM. (1mk)

Find
(a) (i) the length of vector PR. (2mks)

(ii) The height of the pyramid. (2mks)