Transcript Introduction to Vectors

Introduction to Vectors
Lesson 10.3
Scalars vs. Vectors
• Scalars

Quantities that have size but no direction
 Examples: volume, mass, distance, temp
• Vectors

Quantities that have both size and direction
 Examples
Size
• Force
• Velocity
• Magnetic fields
Terminal
point
Initial point
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Vectors
• Representation
B
C

Boldface letters n or S
 Letters with arrows over them m or V or BC
• Magnitude of a vector

Length of the vector, always positive
 Designated |K|
• Equivalent vectors

Same magnitude and
 Same direction
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Resultant Vectors
AB and
• Given vectors
• The resultant vector
(of both vectors added
together) is vector AC
A
AD
D
B
C
• We say AD  AB  AC
• Note that this is the diagonal of a
parallelogram

Can be determined by trigonometric methods 4
Vector Subtraction
• The negative of a vector is a vector with …

The same magnitude
 The opposite direction
-V
V
• So PQ  ST  PQ   ST 
ST
T
P
S
ST
Q
PQ  ST
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Try It Out
• Given vectors shown
• Sketch specified resultant vectors
A
F
D
E
C
B
AB  CD
CD  EF
EF  AB
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Component Vectors
• Any vector can be represented as the sum
of two other vectors
• Usually we represent a vector as
components of a horizontal and a vertical
vector
Also called
"resolving"
a vector
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Position Vector
• Given a point P in the coordinate plane
• P (x,y)
θ
O
• Then OP is the position vector for point P
• Component vectors determined by
Px = |P| cos θ
 Py = |P| sin θ

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Finding Components
• Given a vector with magnitude 16 and
θ = 212°

What are the components?
θ = 212°
16
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Application
• A cable supporting a tower exerts a force
of 723N at an angle of 52.7°
• Resolve this force into its vertical and
horizontal components

Vx = _______

Vy = _______
723N
52.7°
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Magnitude and Direction
• Given horizontal and vertical components
Vx and Vy
 Magnitude found using distance formula
V  Vx 2  Vy 2

Direction, θRef, found with arctan
Ref  tan
1
Vy
Vx
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How Magnitudinous It Is
• Given vector B with Bx = 10 and By = -24
θ=?
|B| = ?
• Determine magnitude and reference
angle.
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Assignment
• Lesson 10.3
• Page 420
• Exercises 1 – 35 odd
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