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.
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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.
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Form 3 MathematicsThe 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) (i) Show that the points Q, T, and R lie on a straight line ( 3 marks)
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Form 3 MathematicsPoint 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
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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Form 3 MathematicsA 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
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
Form 3 Mathematics
Give that OA =2i a + 3 j and OB = 3i -2j, find the magnitude of AB to one decimal place
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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
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.
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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.
answers
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AuthorMaurice A Nyamoti is a Mathematics/ Computer Teacher and has passion to assist students improve grades RSS_FEED
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