Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2019  FebMar  (P19709/12)  Q#5
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Question
Two vectors, and
Where
i. Find the values of
ii. Find the angle between
Solution
i.
We are given that;
If
Therefore, if
We next find the scalar/dot product of
The scalar or dot product of two vectors


Since
Since we are given
Standard form of quadratic equation is;
Its solution is given as;
Therefore, for the given case;
Now we have two options.






ii.
Now we are required to find the angle between
We are given that;
In the case where
To find the angle 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
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