5/6/10 - Noelle

Final New Material of PAP!!!!

Today we started off with a warm up using the first link on the blog to find the sum of vectors:

a) <3,2> + <2,4> = ? = <5,6>

b) <3,2> + <-5,1> = ? = <-2,3>

Then we worked on this problem from the book (which also answered the homework question #69)

Pg. 467 (70)

To solve this you can graph on paper or use geogebra. First you're supposed to find the magnitude of the vectors, which is . From this you can use the pythagorean theorem to find the hypotenuse, which is . Then, by using the law of cosines, set up the following equation: , and by solving algebraically, you get that theta is 90 when cosine of theta is 0.

We went over problem 73 from the homework on page 456:

We discovered you can use vector properties OR use the law of cosines to find the answer. The answer was 398.32 lbs of force at a 12.8 degree angle.

(make sure to try and memorize the formula for the law of cosines for the quiz/test coming up, unless you don't mind the sting of losing a point by asking for it)

*possible test connection, make sure you understand how to do this problem*

Dot/Scalar Multiplication:

if " class="ee_img tr_noresize" eeimg="1" style="vertical-align: middle; "> and " class="ee_img tr_noresize" eeimg="1" style="vertical-align: middle; ">, then .

Scalar is a number, while a vector is a directed line segment. When Vectors are dotted (multiplied together), then they become scalars.

There are 5 Properties of Dot Multiplication that can be found in the book or with detailed explanations at: http://en.wikipedia.org/wiki/Dot_product#Properties.

Angle Between 2 Vectors:

If theta is the angle between 2 vectors, then u*v= (magnitude of u)*(magnitude of v)*cos(theta).

another way to write this is magnitude of u)*(magnitude of v)*cos(theta).

This can be explained in more detail at this site: http://en.wikipedia.org/wiki/Dot_product#Proof_of_the_geometric_interpretation

Things to Remember:

Study for the Quiz on Monday!!!

Test on the 17th!

Supercorrections...

and then the final project!!

Homework: HW #12:

* p. 467/1, 13, 29, 33, 35, 43, 49, 53, 57, 59 (and study)