13.3 - Dot Products and Projections

Hey guys! This is Ilana and Coulter with the notes on 13.3 from Thursday and Friday.

Lisa started off class with the song "Matchmaker" form the movie Fiddler on the Roof.

Lisa explained this by having us figure out who we would best fit with according to certain personal likes and dislikes, such as our opinion of body piercing, sushi and classical music.

We chose a rank between -5 and 5 to represent our views, with -5 as "repulsive" and 5 as "amazing". We used our number for each item as a specified coordinate for a vector: i, j and k. We then milled around the room. For each person we met, we multiplied our i values together, then our j values and ended with the k values. Once we had those three numbers, we added them together to get a single number.

Sounds pretty easy, right?

That is when Lisa told us that that was actually something called DOT PRODUCTS, a scary name for something simple.

We started off class with a bit of review of vector addition and scaler multiplication. We then moved onto Dot Products, also known as vector multiplication, named for the dot used as a multiplication symbol.

It is important to remember that TWO VECTORS ARE PERPENDICULAR IFF THEIR DOT PRODUCT IS ZERO. THEY FORM AN ACUTE ANGLE IFF THEIR DOT PRODUCT IS POSITIVE. THEY FORM AN OBTUSE ANGLE IFF THEIR DOT PRODUCT IS NEGATIVE.

We then went over some properties to keep in mind while dealing with Dot Products. Afterward, we found a useful equation to use to find an angle from the Law of Cosines.

(Keep the projection stuff in mind for later.)

Then, came more practice. After all, practice makes perfect. :)

Now comes the PROJECTION STUFF! Make sure to notice the two equations and how the vecter projection is the scaler projection (component) multiplied by a unit vector.

And, that is where Lisa reminded us that she is first and foremost a physics teacher. :) The last example can be found in the textbook.

Then, came one last (physics related) example before Lisa gave us homework and told us about our QUIZ ON THURSDAY!!!!!!! and that our HOMEWORK IS DUE ON TUESDAY!!!!!!! 

Lisa sent us off with a hint for the last homework problem:

THAT'S ALL FOLKS.

UNTIL NEXT TIME. :)

-Ilana and Coulter