IGCSE

1. VECTORS
OBJECTIVES; By the end of this lesson you should be able to:
- Add and subtract vectors using line segments
- Identify coplanar and parallel vectors using scalar multiple.
- Express coplanar and parallel vectors as ratio.
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2. Match the words to the definitions
• Magnitude
• Scalar
• Resultant
• Vector
• Scalar Multiple
• Displacement
• Velocity
• Column Vector
• speed combined with direction
• a directed quantity
• a single vector which represents
multiple vectors
• a quantity only
• a parallel vector i.e. same direction,
different size
• distance combined with direction
• a vector represented as two vectors
in the horizontal (x) and vertical (y)
directions
• size
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3. Write the following vectors in terms of a and b
1) i) AC ii) FA iii) FD
iv) DC v) AE
  
 
A B
C
D
a
E
F
b
4a
3a
b
(i) AC = a + b

(ii) FA = 3a - b

(iii) FD = b + 3a

(v) AE =

2b - 3a
(iv) DC = a - b

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4. Example 1
A B
CD
i) Show that YX is parallel to AC
ii) What is the ratio YX:AC
AB = r
AD = s
X
Y
AY:YD = 1:2
DX:XB = 1:2
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ABCB is a rhombus

5. Solutions
A B
CD
i) Show that YX is parallel to AC
ii) What is the ratio YX:AC
X
Y
AC = r + s
YX = 2/3r + 1/3(r – s)
r
s
DB = r - s
YX = 1/3(r + s)
i) AC and YX are scalar multiples => parallel
ii) YX : AC = 1 : 3
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6. C
A
B
m
n
P
Write BP in terms of m and n

CA = n + m

BP = - n + ¾ (n + m)

= -¼ n + ¾ m
or
¼ (3m - n)
CP = ¾ CA = ¾ (n + m)
 
Example 2
In triangle ABC, P is a point on
AC such that CP:PA = 3:1
Find BP in terms of m and n
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7. A B
CO
P
6a
6c
Diagram
accurately d
N
2
3
1
3
OP = OC + CP
AP = AC
2
3
6c + (-2c + 2a)
4c + 2a
Rewrite OP in terms of a and cExample 3
Find OP
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