Question

JUST #28. http://screensnapr.com/v/wmqb1W.png

Answer 1

\[\vec u\cdot\vec v=|u||v|\cos\theta\]

Answer 2

Why did you specify the absolute value for a dot product, Turing?

Answer 3

Thats not absolute value, its magnitude.

Answer 4

normally it has two lines around it, but that looks messy on here

Answer 5

He could have put || but yeah :P

Answer 6

Oh, alright.

Answer 7

so just 100*250(pi/6)

Answer 8

no cosine!

Answer 9

no wait thats like 740000 degreees

Answer 10

HHAHAHA I WAS LIKE OMG THIS IS CRAZY

Answer 11

gotta have that cosine or it's not worth the paper it's printed on...

Answer 12

I'm still pretty sure this answer is wrong.. 24998..

Answer 13

let me see what I get...

Answer 14

I got 21650...

Answer 15

21651 rounded

Answer 16

which is reasonable, they are big vectors

Answer 17

u=100, v=250, theta=(pi/6)
100*250=25000*cos(pi/6)=24998.

Answer 18

Calculator is 100% sure in degree too.

Answer 19

perhaps you are in degree mode?

Answer 20

Oh......

Answer 21

lol that's not a good thing

Answer 22

if it's got pi in it you're almost certainly in radians

Answer 23

I was just doing angle between vectors which said make sure it's in degree mode :P

Answer 24

cos(pi/6) is a known special trig value:
\[\cos\frac\pi6=\frac{\sqrt3}2\]and I'm gonna guess the other excercise you did did not have pi degrees in it

Answer 25

Oh! a quick question, how do you find if two vectors are orthogonal or parallel? <15,45>

Answer 26

and <-5,12> sorry :P

Answer 27

again, same formula
if they are parallel what is the angle between them?

Answer 28

And no, it was a different section :)

Answer 29

Isnt it just 15*-5+45*12? 465.

Answer 30

\[\vec u\cdot\vec v=|u||v|\cos\theta\]if u and v are parallel, what is theta?
what about if they are perpendicular?

Answer 31

http://screensnapr.com/v/5gMbRA.png

Answer 32

right, and how did we know those vectors in your example were orthogonal?

Answer 33

equals 0 then vectors are orthogonal

Answer 34

But does 465 mean anything?And how do you know if they are parallel?

Answer 35

besides graphing them of course

Answer 36

can you see why from this formula?\[\vec u\cdot\vec v=|u||v|\cos\theta\]that will answer your question, just answer mine
what is the angle between two orthogonal vectors?

Answer 37

Well they're perpindicular :P

Answer 38

perpendicular.

Answer 39

and a perpendicular angle is how many degrees?

Answer 40

180 or 90.

Answer 41

just 90...
and what is the cosine of 90 degrees?

Answer 42

zero

Answer 43

OH! I get it :D

Answer 44

Not the parallel part but I get the reasoning of the 0.

Answer 45

so when our formula becomes\[\vec u\cdot\vec v=|u||v|\cos\frac\pi2=0\]that's why that works
yeah! so what about parallel? what is the angle there?

Answer 46

pi/2=90 degrees btw...

Answer 47

what is theta between these two parallel vectors?

Answer 48

What..

Answer 49

theta is the angle
what is the angle between them?

Answer 50

Yes, I know, but I have no idea!

Answer 51

you can always draw vectors on top of each other to compare the angleit looks like the angle is 0 degrees (or 180 degrees)
what is the cosine of zero degrees?