VECTORS
A vector is a quantity that hasboth magnitudeanddirection
Examples are force displacement and acceleration
GEOMETRIC DESCRIPTION OF VECTORS
Suppose a particle moves along a line segment from A to B thevector y has
an initial point A thetail andterminal point B the tip and we indicate thisby
writing I AB
7
He can also combine two vectors AB and BE to have the resultantvector
AT
É To get to point c from A we can movefrompoint A
g to B with vector AB and from point B to point Cwith
vector BE
A AB Bc Ad
We now define Yeater Addition and Scalar multiplication
VECTOR ADDITION
If i and I are vectors positioned so the initialpointoff is at the terminal
ut
thenthesum Itf is the vector from the initial point of it totheterminal
port
of f
Triangle Law
II Parallelogram Law
some represent
vector P and I
SCALARMULTIPLICATION
If c is a scalar and I vector then the scalarmultiple of is thevector
whose length is c times thelength of t andwhose direction is thesameas I
it c o and is opposite to 7 if Cao
vector
If c o or to cry on The zero
, I In E É
we can now define difference of 2 vectu
DIFFERENCE OF TWO VECTORS
É T at Cf Its basically vector Addition of it and opposite
directionof F
i Est
II n
our path
COMPONENTS OF A VECTOR
If the initialpoint of a vector at at the origin of a rectanglecoordia
we place
vector at has coordinates of the form
system then the point of a
terminal
9,9
or Ca 92,93 if 30
These coordinates are called
components of a and we conte
at ya ya or at 9,9293
ya Callan
Ca ar93
n
o z
at La y
an
y
a a 92,937
Given thepoints ACK y Z and B ka gu ta the vectra with respresentation
AB is a ka ki yo y Zz t
MAGNITUDE OF A VECTOR
If a a asas then the length of a at a taita
A unitvector is avectorwithmagnitude of 1 an a as as is a unitvector
aptaita
A vector is a quantity that hasboth magnitudeanddirection
Examples are force displacement and acceleration
GEOMETRIC DESCRIPTION OF VECTORS
Suppose a particle moves along a line segment from A to B thevector y has
an initial point A thetail andterminal point B the tip and we indicate thisby
writing I AB
7
He can also combine two vectors AB and BE to have the resultantvector
AT
É To get to point c from A we can movefrompoint A
g to B with vector AB and from point B to point Cwith
vector BE
A AB Bc Ad
We now define Yeater Addition and Scalar multiplication
VECTOR ADDITION
If i and I are vectors positioned so the initialpointoff is at the terminal
ut
thenthesum Itf is the vector from the initial point of it totheterminal
port
of f
Triangle Law
II Parallelogram Law
some represent
vector P and I
SCALARMULTIPLICATION
If c is a scalar and I vector then the scalarmultiple of is thevector
whose length is c times thelength of t andwhose direction is thesameas I
it c o and is opposite to 7 if Cao
vector
If c o or to cry on The zero
, I In E É
we can now define difference of 2 vectu
DIFFERENCE OF TWO VECTORS
É T at Cf Its basically vector Addition of it and opposite
directionof F
i Est
II n
our path
COMPONENTS OF A VECTOR
If the initialpoint of a vector at at the origin of a rectanglecoordia
we place
vector at has coordinates of the form
system then the point of a
terminal
9,9
or Ca 92,93 if 30
These coordinates are called
components of a and we conte
at ya ya or at 9,9293
ya Callan
Ca ar93
n
o z
at La y
an
y
a a 92,937
Given thepoints ACK y Z and B ka gu ta the vectra with respresentation
AB is a ka ki yo y Zz t
MAGNITUDE OF A VECTOR
If a a asas then the length of a at a taita
A unitvector is avectorwithmagnitude of 1 an a as as is a unitvector
aptaita
