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Further Mathematics Paper 2, Nov/Dec. 2008  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments
Weakness/Remedies
Strength
Question 18

(a) The position vectors of the points A, B and C are (4i + 5j), (2i + 2j) and (6i + j) respectively.  Calculate, correct to one decimal place, the acute angle between AB and BC. 

(b) A particle of mass 5kg is suspended by two light inextensible strings making angles 30° and 45° respectively with the horizontal.  Find the tensions in the strings.  (Take g = 10ms-2)

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Observation

This question was also avoided by most of the candidates and the few that attempted it did poorly in it.  From the given position vectors A, B and C, AB = -2i – 3j, BC = 4i-j.   AB. BC = (-2i-3j). (4i-j) = -5.  Thus, -5 = (√13) (√12) cos θ which makes cos θ  = 0.3363. This implies that θ = 109.65°  ~ 109.7°.  Hence, the required angle = 180° – 109.7°  =70.3°.
In the part (b), the resolution of the forces gives.
 
          (-T1 cos  30 )             ( T2 = cos  45)                 (50 cos 90 )          (0)
           (                   )       +    (                     )       +         (                 )     = 
           (  T1 sin  30)               ( T2 sin  45)                     (50 sin 90)           (0)

i.e.  -√3T1  +    √2 T2 +  0 =  0
             2                 2
        1/2 T1 +  √2 T2 + 50  =  0
                            2

Solving the equations simultaneously,
T1 = 36.603N and T2 = 44.829 N

Lami’s theorem could also be applied here.
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