Category: Vectors II

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

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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)

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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

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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)

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Given that position vectors of points A and B are

19/11/2021

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Worked Solution

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

24/9/2020

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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

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

24/9/2020

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Form 3 Mathematics

answer

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

22/9/2020

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Form 3 Mathematics

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

21/9/2020

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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

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

19/9/2020

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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

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

17/9/2020

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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

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

17/9/2020

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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.

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

17/9/2020

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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

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

15/9/2020

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Form 3 Mathematics

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

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

14/9/2020

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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

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