Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2004  MayJun  (P19709/01)  Q#9
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Question
Relative to an origin , the position vectors of the points , , and are given by



and 

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


Since
iii.
We are given that;
A vector in the direction of
Therefore, for the given case;
Expression for the length (magnitude) of a vector is;
Therefore;
Now we have two options;






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