Scribe Post May 7

warm up:

1.
use applet to show:

a) <3,2> + <2,4>
b)<3,2> + <-5,1>

2.
Do p. 457/70

1.
We plugged in the two coordinates for each problem into the applet, and we added them together (found the sum). We observed the movements of the vectors and concluded that...

(vector between two terminal points of two vectors = Terminal - Initial)

A+(-B) = A-B
B-A=-(A-B)

v=i+2j = <1,0> + 2<1,0> = <1,2>
w=2i-j = <2,-1>

for the homework quiz on Monday we must remember:

we reviewed homework problems, and learned that when the magnitude of the vector sum must be 3. This is because the magnitude of cos60º and sin60º is 1. The coefficient of 3 then changes the magnitude's value to 3.

73:
<300,0>

" class="ee_img tr_noresize" eeimg="1" style="vertical-align: middle;">

" class="ee_img tr_noresize" eeimg="1" style="vertical-align: middle;">

to find the vector of A+B use...

because you have found the parallelogram created by the vectors of <300,0> and " class="ee_img tr_noresize" eeimg="1" style="vertical-align: middle;"> . knowing that one side of the parallelogram is 300 and the other is 125 use the given formula above to find the vector/resultant of "x".

Dot Product Notes:

if u= and v= then =u1(v1)+u2(v2)

ex/ u=<3,4> v=<-2,7>

=3(-2)+4.7

=-6+28
=22

p. 460/ 5 properties:

1. =
2.
3.
4.
5.

all variables above are vectors other than: all c's and last "o" in property 2
however, when you "dot" the vectors together your product is a scalar.

definition of "dotted products": take two components multiply them together and then add them

scalar is a real number = 17
vector is a directed line segment = ------>

1st Cool Result:



where theta is the angle between u and v



if = 1, vectors in same direction = parallel
if = -1, vectors in opposite direction = parallel
if = 0, vectors are perpendicular = orthogonal

orthogonal = perpendicular

2nd cool result:

the projection of u onto v (see u, in applet) is given by:

this 2nd cool result will be in class discussion on Tuesday