Form 3 and Form 4
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Transcript of Form 3 and Form 4
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