Download - Triangle law of vector addition
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You’re a tourist in London and want to travel Westminster to Green Park.
How do you get there?
TFL UPDATE: Jubilee Line is Down due to engineering works.
Using the tube how do you reach Green Park now?
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Let the District line from Westminster (W) to Victoria (V) be the vector WV = w .
Green Park (G)
Victoria(V)
w
v
Westminster (W)
Let the Victoria line from Victoria (V) to Green Park (G) be the vector VG = v.
Let the Jubilee line from Westminster (W) to Green Park (G) be the vector WG = g.
g
Westminster to Green park = WG = g
Westminster to Green park = WV + VGand
So WG = WV + VG Then w + v = g
= w + v
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Triangle Law of Vector Additi on
When c = a + b the vector c is said to be the RESULTANT of the two vectors a and b.
By the Triangle Law of Vector Addition:
AB + BC = AC
a + b = c
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A fellow tourist in London asks you how to get from Green Park to South Kensington.
How do you get there?
TFL UPDATE: Piccadilly Line is shut due to broken down train.
Using the tube how do you reach South Kensington now?
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Let Green Park (G) to Victoria (V) be the vector GV = g .
Green Park (G)
Victoria(V)
v
g
Let Victoria (V) to South Ken (K) be the vector VK = v.
Let Green Park (G) to South Ken (K) be the vector GK = k.
Green Park to South Kensington = GK = k
Green Park to South Kensington = GV + VKand
So GK = GV + VK Then g + v = k
South Ken (K)
k
= g + v
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WHICH TWO WAYS GET YOU GET FROM BANK TO LIVERPOOL STREET?
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Let Bank (B) to Moorgate (M) be the vector BM = b
Liverpool Street (L)
Moorgate (M)
b
m
Let Moorgate (M) to Liverpool Street (L) be the vector MV = m
Let Bank (B) to Liverpool Street (L) be the vector BL = l
Bank to Liverpool Street = BL = l
Bank to Liverpool Street = BM + MLand
So BL = BM + ML Then b + m = l
Bank (B)
l
So
= b + m
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AC = AB + BCAC = a + b
AD = AC + CDAD = a + b + c
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i) AB = AO + OB AB = -a + b = b - a
ii) AP = ½ AB AP = ½ ( b – a)
ii) OP = ½ AB + OA OP = ½ ( b – a) + a
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The Triangle Law of Vector Addition
Adding two vectors is equivalent to applying one vector followed by the other. For example,
Suppose a =5
3and b =
3
–2
Find a + b
We can represent this addition in the following diagram:
ab
a + b
a + b =8
1
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Adding Vectors
When two or more vectors are added together the result is called the resultant vector.
In general, if a =a
band b =
c
d
We can add two column vectors by adding the horizontal components together and adding the vertical components together.
a + b =a + c
b + d
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Adding Vectors
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Subtracting Vectors
We can subtract two column vectors by subtracting the horizontal components and subtracting the vertical components. For example,
Find a – b
Suppose and b =–2
3a =
4
4
a – b =4
4–
–2
3=
4 – –2
4 – 3=
6
1
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Subtracting Vectors
To show this subtraction in a diagram, we can think of a – b as a + (–b).
and b =–2
3a =
4
4
ab
a – b
a – b =6
1
–b a –b
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Adding and Subtracting Vectors