Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#9

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Question

Relative to an origin , the position vectors of points  and  are given by


i. 
Given that  is the point such that  , fFind the unit vector in the direction of .

The position vector of the point  is given by , where  is a constant, and it is given that  , where  and  are constants.

ii. Find the values of ,  and .

Solution


i.
 

We are given that

First we need to find .

A vector in the direction of  is;

Therefore, for the given case;

Since;

A vector in the direction of  is;

Therefore;

A unit vector in the direction of  is;

For the given case;


ii.
 

We are given that

Therefore;

It is evident that;

From

We can write;

Substituting this value of  in , we get;

Substituting this value of  in , we get;

Substituting this value of  and   in , we get;

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