Question

Does anyone know Unit vectors and length stuff really well? I'm boggled..

Answer 1

somewhat really well, but kinda sorta maybe like.... sure :)

Answer 2

i and j are unit vectors.... i = <1,0>

Answer 3

Hahaha, okay.
I think I understand how to find length of a vector- that's pretty straight forward. How can I use that kind of math to find a vector parallel to another?

Answer 4

since vectors arent tied to any specific spot, any vector with the same direction is parallel; if they are in the same direction and of the same magnitude they are equal vectors

Answer 5

if the "slope" of the vectors are equal, they are parallel right?

Answer 6

Yeah, okay.
So if I am given a vector in R^4, I solve for it's length, and then what?

Answer 7

Yeah, totally got that.

Answer 8

<4,7> is parallel to <12,21>

Answer 9

Agreed.

Answer 10

r^4?.... 4d stuff eh..

Answer 11

Yeah. That doesn't really matter though, does it? length is length.

Answer 12

distance follows the same rules into other dimensions; you just keep tacking on the extra stuff under the radical.

Answer 13

I'm given a solution here, and they just took 1/(length)*(my original vector)

Answer 14

\[distance of R^n = \sqrt{x^2 + y^2 + z^2 + ......n^2}\]

Answer 15

Yep.

Answer 16

So them multiplying by the reciprocal of my length... Is that just them essentially 'rescaling' my vector, giving me one that is parallel (since it is basically underneath my original? It's on the same spot, but just not as long)?

Answer 17

not to sure about the answer to that.... its been awhile since I got down and dirty with vectors...

Answer 18

Does that make sense, though?
If I took the vector <1, 0, 0, 0> and multiplied it by two, I would get <2, 0, 0, 0>, which is parallel.

Answer 19

that makes sense yes, its magnitude has increased but its direction is the same. it is straight in the air if i see it correctly

Answer 20

Right. But then why would they choose to multiply it by 1/(length)? there must be some significance..

Answer 21

must be, but I would have to review the material that you are getting it from to understand it better :/

Answer 22

Darn. Thanks though!

Answer 23

youre welcome..wish i could have been more helpful :)

Answer 24

It's strange too, since they are telling me to check whether the vector I got had the length of 1...

Answer 25

all unit vectors are of length "1". I recall that much :)

Answer 26

Maybe that's why.. Haha, thanks. Stay tuned. I'm sure I'll be back soon! ;)

Answer 27

and all vectors can be expressed as a sum of their unit vectors and scalars right?

Answer 28

Sheeeeeeeeesh. They wanted it as a unit vector parallel to the original....

Answer 29

Yeah, as a linear combination. Gottttt it!

Answer 30

Thanks!

Answer 31

yay!!

Answer 32

How do I become your fan? Lol

Answer 33

you might have to hit f5 to refresh your browser; but if you want there is a "become a fan" to the side of my name.

Answer 34

:D

Answer 35

lol...thanx ;)

Answer 36

Are you savvy with dot products?

Answer 37

sorta savvy; <xa,ya>.<xb,yb> = xa xb + ya yb right?

Answer 38

Yeah

Answer 39

For this question, I have (xv) . v
And the answer is 2x.

Answer 40

They give me the length of v to be √2

Answer 41

I recall multiplication not being associative with vectors for some odd reason.

Answer 42

Is that just since SQRT(2)*SQRT(2) = 2?

Answer 43

Maybe..

Answer 44

The associative property is meaningless for the dot product because is not defined since is a scalar and therefore cannot itself be dotted. However, it does satisfy the property

(rX).Y = r(X.Y)

for a scalar.

Answer 45

The associative property is meaningless for the dot product because (a.b).c is not defined since a.b is a scalar and therefore cannot itself be dotted. However, it does satisfy the property

Answer 46

i know this means something lol

Answer 47

Okay... so. That gives me X(V.V)=2X, when ||V||=√2

Answer 48

What's the significance of a vector dotted with itself?

Answer 49

WAIT

Answer 50

lets see :)

<1,2>.<1,2>

1(1) + 2(2) = 2+4 = 2(1+2)

Answer 51

1+2 = 1i + 2j right?

Answer 52

If ||V|| = √2, and ||V||= √(V.V), then (V.V)= (||V||)^2!

Answer 53

Where ||V|| is the length of V.

Answer 54

making sense for you :)

Answer 55

But not for you? :P

Answer 56

little bit, but it aint my question lol.

Answer 57

hahahaha, fair nuff!

Answer 58

if the length is sqrt(2) then yes, twice the length = 2

Answer 59

Nooooo. Twice the length is 2√2. Lol. √2 squared is 2.

Answer 60

thats better :) been staring at math too long

Answer 61

Lol. Bedtime!

Answer 62

I think you need to be my fan now..

Answer 63

We all just want to be loved, don't we? Hahahahaha

Answer 64

what? these aint free ya know ;)

Answer 65

Pfffffft

Answer 66

Just trying to get some street cred, yo.

Answer 67

yeah, pupil and 0 is soooo unbecoming these days :)

Answer 68

;)

Answer 69

I do actually have to head out, library is closing up soon... Ciao :)

Answer 70

Adios amigo!