Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/12) | Q#4

Hits: 468

 

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  is;

Therefore for the given case;

Therefore, we need to find .

A vector in the direction of  is;

For the given case;

Hence, unit vector in the direction of (or parallel to) ;


ii.

 We recognize that angle AOB is between  and . Therefore, we need the dot/scalar product of  and .

We are given that;

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

Since ;

The scalar or dot product of two vectors  and  is number or scalar , where  is the angle between the directions of  and  .

where

Therefore, for the given case;

Therefore;

Hence;

Now we can equate the two equations of ;

We are given that angle . Therefore,

Comments