5/5 Scribe Post

Today we started with a warm up involving vectors. The first question was to find the component form, magnitude, and direction angle for vector AB and CD, with given points A(1,1) B(4,-1) C(-5,3) D(-2,1) .
The component form of both the vectors was <3,-2> and the magnitude was . To find the direction angle you create an axis with the initial point as the vertex. The direction angle is then measured counter clock wise. The direction angle is then,, so the two vectors AB and CD are equal. This means that two vectors with the same component form are equal to each other.
Mr. O'Brien showed us the formula to find the component form:
Terminal Point - Initial Point. After this warm up problem we went over problem 59 from the homework. We found out that the component form can be found by , usin> where u was 7/2 for problem 59.


The second warm up question: given u = <2,1> and v = <-1,4>
a. find 3u
b. Graph u and 3u on Geogebra, What do you notice?
c. Repeat a. and b. for u + v
d. Repeat a. and b. for u-v
For this problem we discovered that vector addition is done "tip to tail". So when vector u, vector v and vector u+v are combined they form a triangle. When a vector is multiplied by a number, it is a called a "Scalar multiplication" and it lengthens or shortens the vector.
ex. <3,4> to make a unit vector in the same direction:

Quiz:
After we completed the warm up we discussed the upcoming quizes and tests and decided to review the warm up at the end of class. Next we reviewed the quiz we took last class. Mr. Obrien showed us how to solve problem 1 on the quiz using a calculator only, but wanted to make sure that we could do this problem without a calculator using the sum and difference identity. To solve problem 1 you need to use the sum and difference formulas, then cancel and simply the equation. For problem 2 from the quiz Mr. Obrien recommended that we draw the triangles to start this type of problem. Problems 1 and 2 could both appear on a non-calculator section of a test. Problem 3 you needed to use factoring then an identity to simplify the expression. On problem 4 you needed to remember that there were two answers, . Problems 5 involved using the Area of a triangle formula, A = 1/2 b x h or for this certain problem, A = 1/2 cbsinA. For problems 6 and 7 most people didn't have problems using the double angle formulas and the Law of Sines. The last problem, #8 gave people more trouble. It is important to use the correct fundamental identites.