
VECTORS
(REVIEW)
Vectors
will be used extensively in this course from beginning to end.
If you are not thoroughly familiar with vectors and their addition, subtraction,
and multiplication now is the time to get help.
See a classmate, a tutor in the Physics walkin Tutoring Room, or Dr.
Becker during his office
hours.

Vectors are quantities that have both magnitude and direction. An
direction. An example of a vector quantity is velocity. A velocity
has both magnitude (speed) and direction, say 60 miles per hour
in a direction due west.
(A
scalar quantity is different; it has only magnitude  a time interval
of 10 seconds, for example. No direction!)



Fig.
1.8 Vector C is the sum of vectors A and B.




Vectors can be added:
C = A + B
Vector
C is the vector sum of
vectors A and B, as shown.


Fig.
1.9 The vector sum of two parallel and two antiparallel vectors.





A vector may
be composed of its x and ycomponents as shown. Be careful, the
components of a vector may be positive or negative depending on
whether they are in
the direction of positive or negative axes.


Fig.
1.13 The vector A and its rectangular components.



Vectors
may be multiplied in two ways:
1)
the scalar (dot) product
A o B
2) the vector (cross) product
A x B
The
scalar (or dot) product of two vectors is defined as
A o
B =
A B cos f
= AxBx + AyBy + AzBz
Note:
The dot product of two vectors is a scalar quantity.

Fig.
1.19 The scalar product of two vectors: (
A o B)



The vector (or
cross) product of two vectors is
written as C = A x B
where the direction of the vector product is given by the righthand
rule as shown in the figure.

Fig.
1.22 The direction of the
cross product of two vectors.






The
magnitude of the vector product is given by
C
= C = A x B = AB sin f

Fig.
1.23 The magnitude of the cross product.



© 2013 J. F. Becker


