IGCSE Mathematics Worksheet - Vectors-2

Answer the following

1. 

OPQ is a triangle. T is the point on PQ for which PT : TQ = 2 : 1.
= a and = b.

(a) Write down, in terms of a and b, an expression for .

(b) Express in terms of a and b.  Give your answer in its simplest form.

2. 

ABCD is a parallelogram. AB is parallel to DC. AD is parallel to BC. = p        = q

Express, in terms of p and q

(i)

(ii)

3.

= 2b = 2a = 6a

M is the midpoint of PQ and N is the midpoint of OR.

(a) Find the vector in terms of a and b.

X is the midpoint of MN and Y is the midpoint of QR.

(b) Prove that XY is parallel to OR.

4. (a)Express in terms of a and/orb

(i)   

(ii) 

 X is the midpoint of BC.

(b) Express in terms of a and/or b

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IGCSE Mathematics Worksheet - Vectors

Answer the following
1.

a) Find 3a – 2b

b) Find |a| .

2.


OAB is a triangle and C is the mid-point of OB.
D is on AB such that AD : DB = 3 : 5.
OAE is a straight line such that OA : AE = 2 : 3.
OA = a and OC = c.
(i) Find, in terms of a and c, in its simplest form,
(a) AB

(b) AD

(c) CE

(d) CD

(ii) CE = kCD, Find the value of k

3.


In the diagram, M is the midpoint of AB and L is the midpoint of OM.
The lines OM and AN intersect at L and ON = 13 OB.
= a and = b.
(i) Find, in terms of a and b, in its simplest form,
(a) OM

(b)OL

(c) AL

(ii) Find the ratio AL :AN in its simplest form

4.

       
O is the origin and K is the point on AB so that AK : KB = 2 : 1.
OA = a and OB = b.
Find the position vector of K.
Give your answer in terms of a and b in its simplest form
5.


The diagram shows two points, P and Q, on a straight line AB.
P is the midpoint of AB and Q is the midpoint of PB.
O is the origin, = a and = b.
Write down, in terms of a and b, in its simplest form
(a) AP

(b) the position vector of Q

6. 

OPQR is a parallelogram, with O the origin.

M is the midpoint of PQ.

OM and RQ are extended to meet at S. 

OP=p and OR=r.

a) Find, in terms of p and r, in its simplest form,

(i)OM,

(ii)The position vector of S.

b) When PT= -1/2 p + r, what can you write down about the position of T?

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