Vector
Summary
Notes
,The theory of vectors was developed closely associated with
coordinate geometry.
Scalars are quantities that only have magnitude (no direction)
Vectors are quantities with both magnitude and direction
Examples:
Speed - scalar ; Velocity - vector
Distance - scalar ; Displacement - vector
Mass - scalar ; Force - vector
Representation of Vectors: Line segments can be used to
represent vectors
a) B b)
→
These both have magnitude
and direction
7
^✗
A
>
α is written as AB and b is written as α
Position vectors of a point C are measured relative to the origin as
represented below:
C
od =
r
>
I
0
, Adding and Subtracting Vectors:
Vectors can be added and subtracted, as represented below.
b
✗
y > >
b a
> 7 >
✗+ b
A parallelogram may be used to represent this addition
✗7 3
This shows us that a + b = b + a
Negative vectors:
When subtracting two vectors, we must notes that a - b = a + (-b)
b
>
Vector - b has equal magnitude to vector b but is
b
g- in the opposite direction.
- Same magnitude
b
ib > - Opposite direction
b^ Tx
a-
> > >
Examples: Position vectors OC and OD, determine the vector CD.
> > >
>
CD OD = OC + CD
>
OÉ ,
therefore,
¥ >
> >
CD = OD - OC
Summary
Notes
,The theory of vectors was developed closely associated with
coordinate geometry.
Scalars are quantities that only have magnitude (no direction)
Vectors are quantities with both magnitude and direction
Examples:
Speed - scalar ; Velocity - vector
Distance - scalar ; Displacement - vector
Mass - scalar ; Force - vector
Representation of Vectors: Line segments can be used to
represent vectors
a) B b)
→
These both have magnitude
and direction
7
^✗
A
>
α is written as AB and b is written as α
Position vectors of a point C are measured relative to the origin as
represented below:
C
od =
r
>
I
0
, Adding and Subtracting Vectors:
Vectors can be added and subtracted, as represented below.
b
✗
y > >
b a
> 7 >
✗+ b
A parallelogram may be used to represent this addition
✗7 3
This shows us that a + b = b + a
Negative vectors:
When subtracting two vectors, we must notes that a - b = a + (-b)
b
>
Vector - b has equal magnitude to vector b but is
b
g- in the opposite direction.
- Same magnitude
b
ib > - Opposite direction
b^ Tx
a-
> > >
Examples: Position vectors OC and OD, determine the vector CD.
> > >
>
CD OD = OC + CD
>
OÉ ,
therefore,
¥ >
> >
CD = OD - OC
