Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2013  OctNov  (P19709/12)  Q#4
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Question
Relative to an origin , the position vectors of three points A and B are given by

and 

i. In the case where , find the unit vector in the direction of .
ii. Find the values of for which angle .
Solution
i.
We are given that;
In the case where
A unit vector in the direction of
Therefore for the given case;
Therefore, we need to find
A vector in the direction of
For the given case;
Hence, unit vector in the direction of (or parallel to)
ii.
We recognize that angle AOB is between
We are given that;
The scalar or dot product of two vectors


Since
The scalar or dot product of two vectors
where
Therefore, for the given case;
Therefore;
Hence;
Now we can equate the two equations of
We are given that angle
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