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Further Mathematics Paper 2, May/June. 2008  
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Questions: 1 2 3 4 5 6 7 8 9 10111213 14151617 18 Main
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Question 16

The position vectors of points P, Q and R with respect to the origin are (4; - Sj), (i + 3j) and (-Si + 2j) respectively. If PQRM i~ a parallelogram, find:
            (a)        the position vector of M;
            (b)        I p~1and 1P01;
            (c)        the acute angle between --pr;t and pQ, correct to one decimal place;
            (d)        the area of PQRM.

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Observation

This question was quite unpopular with the candidates. The expected responses were as follow:
Let m ~ [;]. Then RQ ~ MP Le. [~] - [-;] ~ [~5J - [;]
which gives [; ] ~ (=~] which implies that the position vector of m is -2i - 6j.
For the (~art,;;;;" [:::~) - ~5)" [ :::~) thus JPW " v36 + 1 "
Similarly PQ =[ ~] - (-~ = l~J
/PQj = ";9 + 64 = ";73.
Let e be the angle between them,
then [=~. (-~] ~[m J [~ Cos e which gives e = 78.9°.


Area of PQRM =
M Sin e = 51sq.units

 

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