Post on 21-Jan-2016
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CHAPTER 3:VECTORS
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INTRODUCTION
Definition 3.1
a VECTOR is a mathematical quantity that has both MAGNITUDE AND DIRECTION
VECTOR: represented by arrow where the direction of arrow indicates the DIRECTION of the vector & the length of arrow indicates the MAGNITUDE of the vector.
Eg: displacement, velocity, acceleration, force, ect
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INTRODUCTION
Definition 3.2
a SCALAR is a mathematical quantity that has MAGNITUDE only
VECTOR: represented by a single letter s.a, a. Eg: temperature, mass, length area, ect
NHAA/IMK/UNIMAP
INTRODUCTION
Definition 3.3
A vector in the plane is a directed line segment that has initial point A and terminal point B, denoted by, ; its length is denoted by .
ABAB
Initial Point, A
Terminal Point, B
AB
Length: AB
VARIATION OF VECTORS
Definition 3.3
Vectors Negative (Opposite direction but has the same magnitude)
Definition 3.4
Two Equal vectors (If and only if they have the same magnitude and direction)
Definition 3.5
Addition of vectors
The Triangle Law
The Parallelogram Law
The Sum of a Number of Vectors
VARIATION OF VECTORS
Definition 3.6
Subtraction of vectors
Definition 3.7
Scalar Multiplication of vectors
Definition 3.8
Parallel vectors
COMPONENTS OF VECTORS
COMPONENTS OF VECTORS
COMPONENTS OF VECTORS
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MAGNITUDE (LENGTH) OF VECTORS
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MAGNITUDE (LENGTH) OF VECTORS
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MAGNITUDE (LENGTH) OF VECTORS
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VECTOR ALGEBRA OPERATIONS
Definition : Vector Addition and Multiplication by a Scalar
Let and be vectors with k a scalar.
ADDITION :
SCALAR MULTIPLICATION:
321 ,, uuuu 321 ,, vvvv
332211 ,, vuvuvuvu
321 ,, kukukuuk
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ADDITION AND MULTIPLICATION OF VECTORS
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PROPERTIES OF VECTOR OPERATIONS
Let u,v,w be vectors and a,b be scalars:
00)5
0)4
0)3
)2
)1
u
uu
uu
wvuwvu
uvvu
ubuauba
vauavua
uabuba
uu
)9
)8
)7
1)6
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UNIT VECTORS
Definition :
if u is a vector, then the unit vector in the direction of u is defined as:
A vector which have length equal to 1 is called a unit vector.
uu
u
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UNIT VECTORS
uu
u