The position vectors of A and B are respectively. Find the coordinates of M which divides AB in the ration 1: 2 (3mks)Worked Answer: 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.
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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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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.
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Form 2 Mathematics
Vectors r and s are such that r = 7 i + 2 j - k and s = - i + j - k.
Find | r + s |.
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Form 2 Mathematics
The position vectors of points F, G, and H are f, g, and h respectively. Point H divides FG in the ratio 4:-1. Express h in terms of f and g
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Form 2 Mathematics
Given that P = 2i- 3j + k, Q = 3i – 4j- 3k and R = 3P + 2 Q, find the magnitude of R to 2 significant figures.
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Form 2 Mathematics
Given that OA = 2i + 3j and OB = 3i - 2j
Find the magnitude of AB to one decimal place.
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Form 2 Mathematics
Vector 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.
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Form 2 Mathematics
The vertices of a triangle are A(1,2), B(3,5) and C(4,1). The coordinates of C' the image of C under a translation vector T, are (6-2).
(a) Determine the translation vector T. (b) Find the coordinates of A' and B' under translation vector T.
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Form 2 Mathematics
Point D is on AB such that AD = 3 DB.
Express CD as a column vector.
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Form 2 Mathematics
Vector q has a magnitude of 7 and is parallel to vector p. Given that
p= 3 i –j + 1 ½ k, express vector q in terms of I, j, and k.
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Form 2 Mathematics | Topical Questions and Answers
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
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Related Questions on Vectors IFree 1999 K.C.S.E Mathematics Topical Question & Answers Paper 1
A point (-5, 4) is mapped onto ( -1, -1) by a translation. Find the image of (-4, 5) under the same translation.
ANSWER
Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2
In the figure, KLMN is a trapezium in which KL is parallel to NM and KL = 3 NM
Given that KN = w, NM = u and ML = v
Show that 2 u = v= w 
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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
marking scheme
A translation maps a point (1, 2) onto) (-2, 2) . What would be the coordinates of the object whose image is (-3, -3) under the same translation? 2 MARKS MARKING SCHEME
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