VECTORS IN GEOMETRY
STARTER – VECTOR SHAPES
AIM: UNDERSTAND VECTOR NOTATION
The shape is an
isosceles triangle
1)
2
4
2
-4
-4
0
2)
3
2
5
0
-3
-2
-5
0
The shape is a
parallelogram
6
0
-1
4
-3
0
The shape is a
trapezium
3) -2
-4
Try adding the vectors in each question. What
answer do you get each time?
STARTER – VECTOR SHAPES
AIM: UNDERSTAND VECTOR NOTATION
Write the vectors to draw a:1)
Rectangle
2)
Kite
3)
Right-angled triangle
4)
Rhombus
Add up your vectors each time and make sure
that your totals are correct.
VECTOR SHAPES-MULTIPLY BY A SCALAR
Write the vectors to draw a:1) Rectangle
2) Now redraw your rectangle, enlargement
scale factor 2, and write down your vectors
3) Compare your vectors from question 1 and
question 2. What do you notice?
4) Repeat the above drawing a kite and then
enlarging it scale factor 3.
RESULTANT VECTORS – FIND THE
SHORTEST JOURNEY
1) Draw a diagram to show the following journey.
AB =
2
3
BC =
1
-5
2) Now join up A to C and find the vector
AC =
3
-2
RESULTANT VECTORS – FIND THE
SHORTEST JOURNEY
1) AB =
1
3
2) AB =
5
0
3) AB =
-2
4
BC =
3
-1
BC =
0
4
BC =
5
-2
AC =
4
2
AC =
5
4
AC =
3
2
Can you find a quicker way of finding the
resultant vector than drawing the diagram?
MAIN – VECTORS IN GEOMETRY
• Vectors show magnitude (length) and direction
• The symbol for a vector is a bold letter
• Vectors on a coordinate grid are shown by a
column vector
• Vectors are equal if they have the same length
and the same direction. The position of the
vector on the grid does not matter.
• Equal vectors have identical column vectors
• A negative sign reverses the direction of the
vector
MAIN – VECTORS IN GEOMETRY
A
B
C
D
E
F
G
H
I
J
K
L
O
P
Q
R
U
V
W
X
NO = a
OI = b
b
M
N
S
T
a
Find the vectors for:NP = 2a
DE = a
PN = -2a
XU = -3a
OC = 2b
XF = 3b
AM = -2b
DV =
NI =a + b IN = -a-b
PF =2a + 2b
-3b
MAIN – VECTORS IN GEOMETRY
AIM:Write vectors in terms of a,b or a and b
A
D
a
2a
AD = AC + CD
= a + b –2a
= -a + b or
B
BA =
-a
b
AC = AB + BC
= a + b
C
DB = DC + CB
= 2a - b
b - a
AD = AB + BC + CD
= a + b – 2a
= -a + b or b - a
MAIN – VECTORS IN GEOMETRY
AIM:Write vectors in terms of a,b or a and b
a
A
K
B
K,L and M are mid-points of
AB,BC and CA respectively
AB =
b
L
M
C
2a
CA = -2b
BC = BA + AC
= -2a + 2b
= 2b – 2a
BL = ½ BC
=b –a
KL = KB + BL
=a+b –a
=b
What does this
mean about KL
and AC?