Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2012  MayJun  (P19709/13)  Q#2
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Relative to an origin , the position vectors of the points , and are given by


and 

Find
i. the unit vector in the direction of ,
ii. the value of the constant p for which angle .
Solution
i.
A vector in the direction of is;
Therefore, for the given case;
A unit vector in the direction of
For the given case;
ii.
We are given that angle
We are given that;
The scalar or dot product of two vectors


Since
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