**??? - 2015 Q8**

8. With respect to a fixed origin

*O*, the line l_{1}is given by the equationwhere ȝ is a scalar parameter.

The point

(a) Find the coordinates of

The point P has position vector

The point

*A*lies on l_{1}where*ȝ*= 1(a) Find the coordinates of

*A*. (1)The point P has position vector

The line l

(b) Write down a vector equation for the line l

(c) Find the exact value of the distance

The acute angle between

(d) Find the value of cosθ (3)

(e) find the area of triangle

(f) find the coordinates of the two possible positions of

_{2}passes through the point*P*and is parallel to the line l_{1}(b) Write down a vector equation for the line l

_{2}(2)(c) Find the exact value of the distance

*AP*. Give your answer in the form*k*√2, where k is a constant to be determined. (2)The acute angle between

*AP*and l_{2}is θ.(d) Find the value of cosθ (3)

*A*point*E*lies on the line l_{2}Given that*AP*=*PE*,(e) find the area of triangle

*APE*, (2)(f) find the coordinates of the two possible positions of

*E*. (5)