Vectors (Cambridge (CIE) IGCSE Maths: Extended): Exam Questions

Write down two facts about the geometrical relationship between the vectors and .

a parallelogram.
and
is the point on such that

Find , in terms of and , in its simplest form.

.................................................. 

 and .

Write down two statements about the relationship between the points ,  and .

1 ......................................     
2 ......................................     

is a parallelogram.
is the point on  such that .
and .

Find, in terms of and , an expression in its simplest form for .  

= ....................................................

Find, in terms of and , an expression in its simplest form for .  

= ....................................................

is the origin,  and .

Find the position vector of .
Give your answer in terms of and , in its simplest form.

OAB is a triangle and ABC and PQC are straight lines.
P is the midpoint of OA, Q is the midpoint of PC and OQ : QB = 3 : 1.

and .

Find, in terms of and/or , in its simplest form

i) ,

= ................................................... [1]

ii) ,

= ................................................... [1]

iii) ,

= ................................................... [1]

By using vectors, find the ratio .

......................... : ........................

is a parallelogram with diagonals and intersecting at . and .

Find in terms of  and .
Give your answer in its simplest form.

...............................................

The diagram shows a parallelogram .  and . is the midpoint of .

Find an expression, in terms of and , for .
Give your answer in its simplest form.

.................................................

The diagram shows a triangle and a straight line .

and  is the midpoint of .
and .

Find , in terms of  and , in its simplest form.

.................................................

Find , in terms of  and , in its simplest form.

.................................................

is the origin and  is a parallelogram.
is a straight line with .
is a straight line with .
is a straight line and .
and .

Find, in terms of and , in its simplest form,

i) the position vector of ,  

[2]

ii) .  

................................................ [1]

Show that  is parallel to .

is the origin, ,  and  .

and  .

Find, in terms of  and , in its simplest form .

...................................................

Find, in terms of and , in its simplest form the position vector of .

is a parallelogram and is the origin.  and . is the midpoint of . and     Find  in terms of p and q, giving your answer in its simplest form. 

............................................

Find the position vector of  in terms of p and q, giving your answer in its simplest form. 

is a parallelogram with  and .
is a straight line with .
is a straight line with .

Write , in terms of  and , in its simplest form.   

..............................................

The straight line  cuts  at 
is the midpoint of .

Find the value of .   

= .............................................

In the diagram,  is a parallelogram. and intersect at  and .
and .

Find , in terms of  and , in its simplest form.  

................................................

i) Find , in terms of  and , in its simplest form.

 ................................................ [2]

ii) Find .

................... : ................... [2]

  and  .  
Find the positive value of .

..............................................