Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2011  OctNov  (P19709/12)  Q#3
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Question
Relative to an origin , the position vectors of points A and B are given by

and 

where is a constant.
i. Find the value of
ii. In the case where
Solution
i.
We recognize that angle AOB is between
We are given that;
The scalar or dot product of two vectors


Since
Angle AOB=
If
Therefore, we need to equate scalar/dot product
ii.
We are given that;
When
A vector in the direction of
Therefore to find
Expression for the length (magnitude) of a vector is;
For the given case;
But we are looking for a vector in the direction of
A unit vector in the direction of
For the given case;
Hence desired vector in the direction of
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