Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/13) | Q#2

Hits: 273

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

and

Find

    i.      the unit vector in the direction of ,

ii.   the value of the constant p for which angle .

Solution


i.
 

A vector in the direction of  is;

Therefore, for the given case;

A unit vector in the direction of  is;

For the given case;


ii.
 

We are given that angle  , hence,  and  are perpendicular and therefore their dot/scalar product is equal to ZERO.

We are given that;

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

Since ;

Comments