Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/13) | Q#4
Relative to an origin O, the position vectors of points A, B and C are given by
The point P lies on AB and is such that .
i. Find the position vector of P.
ii. Find the distance OP.
iii. Determine whether OP is perpendicular to AB. Justify your answer.
We are given that;
We need to find and .
A vector in the direction of is;
Expression for the length (magnitude) of a vector is;
We have found in (i) that;
If and & , then and are perpendicular.
Therefore to determine whether OP is perpendicular to AB or not, we need to find out scalar/dot product of and .
The scalar or dot product of two vectors and in component form is given as;
For the given case, we have found in (i) that;
Since , vectors and are perpendicular.