Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2014  MayJun  (P19709/11)  Q#8
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Question
Relative to an origin , the position vectors of the points and are given by

and 

i. Find the value of p for which angle is .
ii. For the case where , find the unit vector in the direction of .
Solution
i.
We are given that angle , hence, and are perpendicular and therefore their dot/scalar product is equal to ZERO.
The scalar or dot product of two vectors and


Since
Now we have two options.








Not possible 

ii.
In case

and 


and 

A vector in the direction of
Therefore, for the given case;
Expression for the length (magnitude) of a vector is;
Therefore;
A unit vector in the direction of
For the given case;
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