TOPIC 1

POLygon II

HOW IS RELATE TO VECTOR???

Look at this example…

Example 1:

In the diagram, and are paralellogram. 9 and 6 .

Determine, in terms of and

PQST PQRS PQ p PT q

p q

= =uuur uuur

P

Q

TS

R

9 p:

6q:

Non-parallel vector

)

)

a PS

b PR

uuur

uuur

SOLUTION:

9 6

9 (9 6 )

18 6

PS PQ PT

p q

PR PQ PS

p p q

p q

= += +

= += + +

= +

uuur uuur uuur

uuur uuur uuur

Parallelogram Law

Polygon is used in addition and subtraction vector to make it more understand

to solve the problem. That why polygon is relate to this subtopic

Another example…..

In the diagram, is a parallelogram. is the midpoint of .

Given that, 8 and 6 , determine each of the following

vectors in terms of and

PQRS T SR

PQ a PS b

a b

= =uuur uuur

P

Q

R

TS

)

)

)

a SQ

b QT

c PS RS−

uuur

uuur

uuur uuur

After this, you will see polygons is relate so much in the topic vector. Hope you will better understand after this.

SOLUTION:

( ))

8 6

a SQ PQ SP

PQ SP

a b

= +

= + −

= −

uuur uuur uur

uuur uur ( )( )

)

18 6

2

b QT QS ST

ST SQ

SR a b

= +

= + −

= − −

uuur uuur uuur

uuur uuur

uur

( )

( ) ( )

18 6

21

8 8 624 8 6

6 4

PQ a b

a a b

a a b

b a

= − −

= − −

= − += −

uuur

( )

) 6

6

6

6 8

c PS RS b RS

b QP

b PQ

b a

− = −

= −

= − −

= +

uuur uuur uuur

uuur

uuur

Triangle Law

ST and SR

are parallel

and ST=

1

2SR

PQ SR=uuur uur