PPast Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#5

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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 the  for which  is perpendicular to .

   ii.       Find the value of the  for which magnitude of   is 7.

Solution


i.
 

If  and  & , then  and  are perpendicular.

Therefore we need to find the scalar/dot product of   and  and equate it with ZERO. We are given that;

The scalar or dot product of two vectors  and  in component form is given as;

Since ;

For the given case;


ii.
 

We are given that;

A vector in the direction of  is;

For the given case;

Expression for the length (magnitude) of a vector is;

Therefore;

We are given that;

Therefore;

Now we have two options;

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