Add. Math. Form 5 : Chapter 4 Vector

1. SPM2005/2/6In the diagram, ABCD is a quadrilateral. AED and EFC are straight lines.

It is given that , , ,

and .

(a) Express in terms of and/or :

(i) ,

(ii) , [3 marks]

(b) Show that the points B, F and D are collinear. [3 marks]

(c) If and , find [2 marks]

2. SPM2006/2/5The diagram shows a trapezium ABCD.

It is given that , , and

.

(a) Express in terms of and . [2 marks]

(b) Point F lies inside the trapezium ABCD such that , and m is a constant.

(i) Express , in terms of , and .(ii) Hence, if the point A, F and C are collinear, find the

value of m. [5 marks]

3. SPM2007/P2/8 4. SPM 2008/P2/6 ( 7 marks)

Diagram 3 shows triangle AOB. The point P lies on OA and the point Q lies on AB. The straight line BP intersects the straight line OQ at the point S. It is given that ,

, ,

(a) Express in terms of and / or :

(i) , (ii) . [ 3 marks]

(b) Using and , where h and k are constants, find the value of h and of k. [5 marks]

(c) Given that units, units and ,

find . [2 marks]

In Diagram, ABCD is a quadrilateral. The diagonals BD and AC intersect at point R. Point P lies on AD.

It is given that , , and

.

(a) Express in terms of and :

(i) ,

(ii) .

(b) Given that and , where h and k are constants, find the value of h and of k.