# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2004 | May-Jun | (P1-9709/01) | Q#9

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Question

Relative to an origin , the position vectors of the points , , and are given by      and  where and are constants. Find
i.
the unit vector in the direction of ,

ii.      the value of p for which angle ,

iii.       the values of for which the length of is 7 units.

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.

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

We are given that; A vector in the direction of is; Therefore, for the given case; Expression for the length (magnitude) of a vector is;  Therefore;          Now we have two options;            