Physics 204A Class Notes
31
Section 3 – Vectors
Section Outline
1.
Vectors
2.
Components of a Vector
3.
Addition of Vectors
4.
Multiplication of Vectors
Vectors are a mathematical tool.
Like all math tools, they seem unnecessarily difficult and not too
helpful at first.
However, after they have been mastered, they turn out to be a great convenience.
1. Vectors
Scalar: A quantity with a magnitude only.
Vector: A quantity with magnitude and direction.
Example 3.1: A hiker walks 20.0m NNE.
Sketch this vector.
The vector as shown at the right.
The length of the vector is
proportional to the magnitude (20.0m) and the arrow indicates
the direction.
Note that vectors can be moved with respect to the origin as long
as neither the magnitude nor direction is changed.
A way to right this vector is,
r
r
=
[email protected]˚ N of E
.
This method is cumbersome.
We will learn a
better way soon.
Note:
The book uses bold type face for vectors (
r
=
r
r
).
2. Components of a Vector
Example 3.2: A hiker walks 20.0m NNE.
Find the distance she has gone northward and the
distance eastward.
Convert these polar coordinates to Cartesian,
y
=
r sin
!
=
20.0sin67.5˚
"
y
=
18.5m northward
and
x
=
r cos
!
=
20.0cos67.5˚
"
x
=
7.65m eastward
.
These parts of the vector are called “components.”
Unit Vectors:
ˆ
i
≡
1 unit along the xaxis,
ˆ
j
≡
1 unit along the yaxis and
ˆ
k
≡
1 unit along the zaxis.
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 Fall '09
 Kagan
 Physics, Vectors, Dot Product, Ax Ay Az, Physics 204A Class, 204A Class Notes

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