TING. 3 (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

P

Q

T S

R

9 p

6q

Non-parallel vector

)

)

a PS

b PR

SOLUTION:

9 6

9 (9 6 )

18 6

PS PQ PT

p q

PR PQ PS

p p q

p q

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

P

Q

R

TS

)

)

)

a SQ

b QT

c PS RS

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

)

18 6

2

b QT QS ST

ST SQ

SR a b

18 6

21

8 8 624 8 6

6 4

PQ a b

a a b

a a b

b a

) 6

6

6

6 8

c PS RS b RS

b QP

b PQ

b a

Triangle Law

ST and SR

are parallel

and ST= 1

2SR

PQ SR

TING 3 (TOPIC 2)

LINE & ANGLES II(ANGLES ASSOCIATED WITH TRANVERSALS AND PARALLEL

LINES)

A tranversal is a straight line that intersect two or more straight line The figure shows two parallel lines AC and DF intersected by the tranversal MN

Parallel line are lines on the same plane that never met, no matter how far

they extended When two lines are intersected by a tranversal,they are parallel if

a) the corresponding angles are equal

b) the alternate angles are equal

c) the sum of interior angles is 1800

A CD F

N

M

We can use the knowledge about concept of parallel line related to the topic vector

especially in addition and subtraction of vector.

Addition of vector

For example:

a

b

c

The vector is the resultant of the

vector and is represented

mathematically as .Note

that the vector has the same direction

and

ca

b c a b

c a b

The example above for the addition of vector that is parallel.There are many example that can relate the concept parallel line to addition and subtraction of vector.

Example 2

In the diagram , PQRS is a trapezium with PQ parallel to SR. Given that

P Q

RSS

4, 3 and 4 . Find

3

a)PQ in terms of

b) PQ

SR PQ PQ m m units

SR m

SR

Solution:

4

34

34

3 43

Hence,PQ 3 4

=7

SR PQ

SR PQ

SR m m

SR m m

m

b) 7 4

= 28

PQ SR

units

PQ and SR are parallel

Magnitude of the resultant vector

and PQ

SR

TING 3 (TOPIC 3)

ALGEBRAIC EXPRESSION III

Multiplication algebraic without simplication

Multiplication algebraic involving denominator with one term

For example : Find

WHAT IS THE RELATIONSHIP BETWEEN

ALGEBRAIC EXPRESSION AND VECTOR???

2 53 and 2

4

cb m n r

d

Multiply algebraic expression with numerator

We use algebraic expression to solve problems especially in addition and subtraction vector. Obviously, it use algebraic expression when to express any vector in any term such as in terms of and p

q

Now,let take a look at this example…..

Algebraic expression is related to this subtopic vector

(addition and subtraction of vector)

In the diagram, PQR is a triangle. T is a point on RQ such that 2RT= 3TQ and

S is a point on PQ such that 4PS = SQ. Given that

determine each of the following vectors in terms of and

5 and 4PQ a PR b

P

S

Q

T

R

a

b

)

)

a SR

b TS

a) Given 4

4

4

5

1

51

55

PS SQ

PS SQ

PS SQ PQ

PS PS SQ

PS PQ

PS PQ

a a

4

PS SR PR

SR PR PS

b a

Expand single bracket with

one term

)

25 4

58

2 458

2 45

82

5

b TS TQ QS

a b SQ

a b PS

a b a

a b

Expand and

multiply two

algebraic

terms with

fraction

Thus, as we can see from the example above subtopic addition and subtraction of vector is

connected to the algebraic expression as we always use to solve problem relate to vector

TING 4 (TOPIC 1)

THE STRAIGHT LINE

The straight line is a line that does not curve. In geometry a line is always

a straight (no curve).

In coordinate geometry, lines in a Cartesian plane can be described algebraically by linear equations and linear functions. In two dimensions, the characteristic equation is often given by the slope-intercept form:

where:

m-slope of the line

c- the y-intercept of the line

x- the independent variable of the function y

The examples of straight line

The concept of straight line is used in the topic vector.

WHY???....BECAUSE vector also is a straight line dan doesn’t have a curve.

That is main properties of vector, STRAIGHT LINE.

How it relate to the subtopic vector (addition and subtraction of vector)???

Let, take a look at it now….

The diagram shows the vectors . Express it terms of and a b

and a b

E

F

H

a

bG

)

)

a EF

b GH

) 3a EF a b

SOLUTION:

E

F

3a

b

Resultant

vector

G

2b

a

H

) 2

2

b GF a b

a b

Subtraction

of vector

Thus, the straight line is the basic concept of vector. By knowing the knowledge of

straight line, we know the direction and magnitude of the vector that can be used in the subtopic

(addition and subtraction of vector). That why, STRAIGHT LINE is important to vector