Vectors and Transformations
http://physics.oregonstate.edu/portfolioswiki
Corinne Manogue
Tevian Dray
5 October 2010
XIII SEMANA DE LA ENSENANZA DE LA FISICA
5 October 2010
XIII SEMANA DE LA ENSENANZA DE LA FISICA
Representations
• Write down on your whiteboard a
representation of a vector.
5 October 2010
XIII SEMANA DE LA ENSENANZA DE LA FISICA
What Are Vectors?
Mathematics:
• Triples of numbers
v  v1 , v2 , v3
5 October 2010
Physics:
• Arrows in space
v  v1 ч v2 ш v3kˆ
XIII SEMANA DE LA ENSENANZA DE LA FISICA
Dot Product
• Write down on you whiteboard something
that you know about the dot product.
5 October 2010
XIII SEMANA DE LA ENSENANZA DE LA FISICA
Group Activity
• Emphasizes that vectors are arrows
• Combines geometry and algebra
• Uses multiple representations
geometry: u  v  u v cos


algebra:
u  v  u1 ч u2 ш u3kˆ  v1 ч v2 ш v3kˆ
memory:
u  v  u1v1  u2 v2  u3v3
5 October 2010

XIII SEMANA DE LA ENSENANZA DE LA FISICA
Sample Group Activity
Find the angle
between a
diagonal of a
v

5 October 2010
u
cube and an edge
XIII SEMANA DE LA ENSENANZA DE LA FISICA
Sample Group Activity
v

u
u  ч ш kˆ
v  kˆ
u v
1
cos( ) 

3
u v
5 October 2010
XIII SEMANA DE LA ENSENANZA DE LA FISICA
Grid
• On your
whiteboard,
make a grid
like this.
• We will
draw a
vector k
on your grid.
5 October 2010
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XIII SEMANA DE LA ENSENANZA DE LA FISICA
For each of the points on your grid:
• Draw the position vector r
• Calculate k  r
• Connect the points for which k  r
is a constant.
5 October 2010
XIII SEMANA DE LA ENSENANZA DE LA FISICA
• Describe

cos k  r
5 October 2010

XIII SEMANA DE LA ENSENANZA DE LA FISICA
• Describe

cos k  r  t
5 October 2010

XIII SEMANA DE LA ENSENANZA DE LA FISICA
• Describe

E0 cos k  r  t
5 October 2010

XIII SEMANA DE LA ENSENANZA DE LA FISICA
The Future
Instructor: …How do you imagine your future careers to be?
S2: Kind of like this class, I think, is what I imagine my future career to be
if it’s research or something
Because you’re not given a set homework or list of things to do
And honestly this class probably prepares me a lot more for my job
than a rote memory, like a strictly lecture type of class
because my life is not going to be a lecture
and my like work I take home with me is not going to be homework
In strictly the sense that you pull it out of a book to get the answer (?)
Let’s turn to page 675, here the answer really is
It’s like you’re exploring things
And you’re trying to find the answer using whatever method you have
And if that method is like
“oh I’ll use angle (?) to find like whatever the graph is supposed to be like”
and “Oh we have to take it out to the 100th term to see like
“Oh it really does (?) this graph”
and that’s just the way it’s going to be.
5 October 2010
XIII SEMANA DE LA ENSENANZA DE LA FISICA
Flux Maple Worksheet
• Initially, define the location of the point charge to
be at the origin of a rectangular coordinate system:
• > Point:=[0,0,0];
• > a:=Point[1];b:=Point[2];c:=Point[3];
• Find the electric field of the point charge:
• > r:=sqrt((x-a)^2+(y-b)^2+(z-c)^2);
• > Efield:=(q/(4*Pi*epsilon))*grad(-1/r,[x,y,z]);
5 October 2010
XIII SEMANA DE LA ENSENANZA DE LA FISICA
Flux Maple Worksheet
5 October 2010
XIII SEMANA DE LA ENSENANZA DE LA FISICA
Plane Wave Activity
Students connect points
with equal value of
k r
What is

cos k  r   t
5 October 2010

XIII SEMANA DE LA ENSENANZA DE LA FISICA
Plane Wave Representations
5 October 2010
XIII SEMANA DE LA ENSENANZA DE LA FISICA
Multiple Representations
Write on your small white board something about
dot products.
u  v  u1v1  u2 v2  u3v3
v
u  v  u v cos
u  u u
5 October 2010
v u
u
u
XIII SEMANA DE LA ENSENANZA DE LA FISICA
Small White Board Questions
• Allow the instructor to see if everyone is on
the same page.
• “Quiet” members of the class are
encouraged to participate.
• Students vie to have their answers chosen.
• Keep everyone engaged and awake
5 October 2010
XIII SEMANA DE LA ENSENANZA DE LA FISICA
Large Whiteboards
• Provide the opportunity:
– to compare and contrast answers,
– for mini-presentations,
– to discuss problem-solving strategies, synthesis,
evaluation, decision-making, etc.
5 October 2010
XIII SEMANA DE LA ENSENANZA DE LA FISICA