Question

Find the following using the given vectors: a=<1, 1, -2>, b=<3, -2 , 1>

a) a*b b)Find the angle between vectors a
and b.

c) Find the unit vector parallel to b d)axb


I found a, b, and d. I am not sure how to solve part (c)

Answer 1

I THINK we need to find the projection of u onto v here. So we're looking for vector components. The projection of u onto v is
\[(\frac{ u\dot~v }{ ||v||^{2} })*v\]

Answer 2

Because when we find vector components, one component is parallel and the otheris orthogonal.

Answer 3

we have not learned about projections yet...

Answer 4

Oh O.o I see, lol. Whoops!

Answer 5

well, we won't be going over projections since we ran out of time. Lol

Answer 6

Is that the formula?

Answer 7

let me read up on this and i will get back to you guys.

Answer 8

Yeah, to find
\[proj _{v}u\] projection of u onto v, which can bewritten as just
\[w _{1}\]The second component, the one orthogonal to the vector is:
\[u-w _{1}\]
And alright, go for it, lol.

Answer 9

so what is the difference between the scalar projection and vector project? I see the formulas are quite a bit different

Answer 10

Oh nvm I just read it. Lol

Answer 11

Okay I got this

Answer 12

Lol, awesome. Yeah, otherwise you'd justinvent yourown vector, but the components let you find a parallel and an orthogonal component. Oh, hey, you're at the beginning of calc 3, right?

Answer 13

do you know how to invent your own vector?

Answer 14

I am at the end of calc 3

Answer 15

Not really, lol. But I wouldthink that all you'd need to do is shift each coordinate up 1, haha. But that's cheating.

Answer 16

we were introduced diff eqs and vectors

Answer 17

Ah. Yeah, I noticed you're doing stuff I didin calc 2. But I was curious because I have the textbook for calc 3 and am just starting it. I wanna keep up with ya, it'd be awesome to have someone studying the same stuff xD

Answer 18

yeah for sure. i am starting calc 4 fall term

Answer 19

Ah. I don't think we even have a calc 4 here. Calc 3 is highest. But nah, if we have the same material I'd wanna keep up and learn it as you do.

Answer 20

calc 2 was by far the most interesting calc class. I liked engineering and physics apps as well as volumes

Answer 21

I suck with word problems, haha. I did horribly with some of the mixture ones xD

Answer 22

But maybe thats why we don't have calc 4, we cover more in calc 2.

Answer 23

i love application. Did you guys ever talk about exponential growth and decay?

Answer 24

Yep, definitely. Those were np.

Answer 25

calc 4 is only vectors.

Answer 26

I see. Lol, the beginning of my calc 3 text is vectors.

Answer 27

are you in college or high school?

Answer 28

College. I'm a math tutor where I go to school. I'm just the least experienced one there, lol.

Answer 29

Nice, I was considering signing up to be a math tutor at my school but i don't have time. what college do you go to?

Answer 30

I'm in Vegas. I'm going to start my first semester at UNLV on the 26th, so I'll be doing part time at College of Southern Nevada and UNLV. One of the plans in mind, though:
東京でテンプル大学に入るつもりです。
Plan on studying at a university in Tokyo. I don't wanna stay in Vegas, haha.

Answer 31

Why Tokyo and what are you studying?

Answer 32

Well, Tokyo is a Japanese university, but it's home school is Temple, which is in Philadelphia. Not only am I studying math, but also Japanese. I wanna leave Vegas and just be able to actually see Japan. I thought it'd be fun to study there and, since its a branch of an American uni, I can still get financial aid and other benefits that U.S students normally get.

Answer 33

Bleh, *in Tokyo

Answer 34

Oh very nice. One of my buddies has about a term left until he gets his BS in mathematics. in fact he is on this site. You could pick his brains when you see him.

Answer 35

Right. I'm working on becoming a math teacher, so this site is awesome experience and review.

Answer 36

he knows a crap load of math. He actually tutors me at my school, very smart guy

Answer 37

have you taken any analysis math courses or abstract algebra courses?

Answer 38

A lot of the people on this site are geniuses, lol. Even some of the people we help are geniuses considering we're helping them woith calc 3 and Diff EQs material.

Answer 39

I'm about to. Going to take Discrete Math along with Diff EQs in 10 days xD

Answer 40

i won't rake diff eqs until next spring.

Answer 41

And I wont offically take calc 3 until spring, but I have the text and am studying. So if you're going to do the same material then that's great. I'm looking at a section about determining the distance from a plane to a point not on theplane.

Answer 42

are you going to be learning about sequence and series in calc 3?

Answer 43

Did all of that in calc 2 already.

Answer 44

I see.. lol well i didn't like series. Power and tayler series isn't too bad though

Answer 45

Some of them get tricky for sure, lol. I just need practice on them.

Answer 46

well, I am going to solve this vector problem, appreciate the help and good luck to you!

Answer 47

Alright, let us know if you need the help :3

Answer 48

so i got <-1/6, -1/6, 1/3>

Answer 49

Before I even check the answer myself it has to be wrong. It must be a unit vector, which means \[a ^{2}+b ^{2}+c ^{2} = 1\]

Answer 50

what do you mean? I manipulated the problem wrong?

Answer 51

Seems so.

Answer 52

it's all your fault=P

Answer 53

Hmm.....Okay, my bad, we didn't finish the problem. You still need to check your math on thefirst part, though xD This portion wasn't supposed to give us a unit vector, only the regular vector. But I still got a different answer. The vector I came up with was
<-3/14, 2/14, -1/14>

Answer 54

what did you get for the mag of a?

Answer 55

We don't use mag a, we use mag b.

Answer 56

oh so we are looking for the projection of a onto b?

Answer 57

Right.

Answer 58

okay well there is my problem...

Answer 59

Nope, my problem, you were right, didn't notice it said b x_x

Answer 60

soooo my math isn't wrong?

Answer 61

Nope, just checked it.

Answer 62

I just chose the wrong projection.

Answer 63

Alright, so now we just need to divide this vector by it's magnitude to get the unit vector.

Answer 64

mag of a, right?

Answer 65

magnitude of the resulting vector. So the 1/6 vector you had.

Answer 66

shoot, i just erased all my work. lol

Answer 67

Okay, got the answer, just needed to check it x_x

Answer 68

yeah, we have the correct vector, which is the projection you came up with, but if we want the unit vector version of it, we need to divide it by its own magnitude.

Answer 69

for the first one i get -sqrt14/84

Answer 70

For thei component?

Answer 71

wait by vector b or vector a mag?

Answer 72

yeh for the i comp

Answer 73

So we have the vector <-1/6, -1/6, 2/6> So now we divide this vector by it's magnitude:
\[\sqrt{(\frac{ -1 }{ 6 })^{2}+(\frac{ 1 }{ 6 })^{2}+(\frac{ 2 }{ 6 })^{2}}\]
\[\frac{ \sqrt{6} }{ \sqrt{36} }=\frac{ \sqrt{6} }{ 6 }\]
That should be the magnitude you come up with. If that makes sense o.o

Answer 74

i got 0

Answer 75

O.o Do you see where I got my work from, though?

Answer 76

yeah i see what you did there

Answer 77

Yeah, that would be the process. Then you divide your vector by that magnitude:
\[\frac{ proj _{b}a }{ ||proj _{b}a|| }= (<\frac{ -1i }{ 6 },\frac{ -1j }{ 6 },\frac{ 2k }{ 6 }>)*\frac{ 6 }{ \sqrt{6} }\]

Answer 78

your are mult?

Answer 79

Well, I flipped the fraction to multiply it.

Answer 80

Instead of sqrt(6)/6 and dividing by that, I just flipped it to multiply.

Answer 81

ah yes you did

Answer 82

And then multiplying that through would give you your unit vector :3

Answer 83

i still get 0

Answer 84

During the magnitude part?

Answer 85

hold on here

Answer 86

lol, kk

Answer 87

<-sqrt6/6,-sqrt6/6, sqrt6/6>

Answer 88

Last one is sqrt(6)/3 :P

Answer 89

i reduced it when i use the projection formula

Answer 90

so ha=P

Answer 91

whatev xD As long as you got the right answer, lol.

Answer 92

i don't have a solution yet. these are on a pre-exam handout

Answer 93

Ah. Well I just didn trationalize the denominator on mine. Depending on the professor there's no need to.

Answer 94

kk

Answer 95

Mhm. When we don't mess up hopefully it makes sense xD

Answer 96

okay cool. Thanks again for walking me through the problem.

Answer 97

yep, np. And im still dealing with vectors so maybe I can help out som emore xD Gotta pack up, though, Ill be back soon.

Answer 98

yeah okay, later