You should be able to solve this

Do your own homework, OP

Those have a name, use it next time.
I may act autistic but at least I don't just spout shit without proof.

tfw to stupid to solve basic problems

>what are position vectors?

"My knowledge of vectors come from Vsauce HURR"

position vectors are just vectors that describe a particles position. They can still be parallel transported and no two vectors cannot be parallel nor intersecting.
No

curious
How did you determine that

>no two vectors cannot be parallel nor intersecting
When are you going to realize how false this is?

Does the vector from (0,0) to (1,1) intersect the vector from (5,5) to (4,3)?
Are they parallel?

>They can still be parallel transported and no two vectors cannot be parallel nor intersecting.
CS-major confirmed. Kill yourself now

explain pls

AC//BD implies AB//CD
So no.

>what is a trapezoid

doesn't prove that
AC//BD => ||NM|| = 1/2 (||AC|| + ||BC||)
unfortunately

When you show me a reason to.
The dot product between those two vectors is 1*1+1*2=3=sqrt(2)*sqrt(5)*cos(theta)
There exists a nonzero angle between the two vectors, therefor they cannot be parallel and must intersect.
I don't know why you think I'm a CS major. Are you projecting? I'm just using what I learned in linear algebra. Is there something I'm not getting here? Certain terminologies exist for a reason. You cannot have a vector that's "locked into place" unless you define a new origin, but then why the fuck would you talk about two vectors with two different origins without clarifying that in the problem? Just say line segment next time if that's what the problem is discussing.

yes it does

you're right

>When you show me a reason to.
You meant to say position vectors relative to the same defined origin (such as (0,0,0)) cannot be parallel while not intersecting entirely. If you meant to say that, you are correct. However, not all vectors are positioned relative to the same point. For example, there can be a position vector ( x y z ) whose origin the point ( 7 8 2 ) parallel to a position vector whose origin is ( 0 0 0). Therefore these vectors are parallel and do not intersect

you realize that if we are talking about vectors interesecting, then it is obvious that we are talking about vectors that might or might not have (0,0..,0) as origin?
otherwise ALL vectors interesect at the origin.

Stop wasting your time with that user. He doesn't understand basic logic

>Doesn't deny being a CS major
Kek

CS brainlet BTFO

What about two vectors at the same origin and same direction but different lengths? Would they be intersecting or parallel? It's nonsense to use terms that don't apply to vectors when discussing vectors.

I understand basic logic, I just also understand how to use correct terminology.

I'm a math/physics double major. And I wasn't BTFO, that user either didn't read my full post or just rehashed exactly what I said then claimed I was wrong.

>It's nonsense to use terms that don't apply to vectors when discussing vectors.
Explain

>that user either didn't read my full post or just rehashed exactly what I said then claimed I was wrong.
Explain your initial and ridiculous claim

>I'm a math/physics double major
Well you're pretty damn stupid for a math/physics double major

Being parallel implies non-intersecting, yet the two vectors I described seem to be doing both. It is pointless to discuss if a vector intersects another because all vectors intersect at the origin.

At the end of my post I talked about how pointless it is to define different origins for different vectors in the same problem when you could just use terms like line segment to more correctly describe the object. The other user then went on to "prove me wrong" using the concept of different origins. So either he read my full post and got the idea from me and tried turning it against me, or he didn't read my full post and used a concept that I shit on minutes earlier.

How so? You have yet to show me anything other than your lack of knowledge of simple definitions.

>all vectors intersect at the origin.
Holy kek user, you cannot be this stupid

Am I being trolled?

>At the end of my post I talked about how pointless it is to define different origins for different vectors in the same problem when you could just use terms like line segment to more correctly describe the object
That's irrelevant. This entire argument here is happening because you made the claim "Two vectors cannot be neither parallel nor intersecting, because vectors don't have an inherent position in space and can be parallel shifted wherever you want them to be", which to anyone with even some knowledge of linear algebra IS ABSOLUTELY RIDICULOUS.

>Two vectors cannot be neither parallel nor intersecting,
Seems reasonable.

But how do planes exist?

Why is it absolutely ridiculous? What bit of linear algebra knowledge makes it absolutely ridiculous? This is why I asked if I'm missing something. Nobody has given me a straight answer so I'll just assume I'm being trolled.

Look at this answer:

The Wright brothers.

Again, am I missing something? Why does the existence of a plane mean that vectors can't be parallel transported?

Is this b8 or do you not know what a (geometric) plane is?

>Why does the existence of a plane mean that vectors can't be parallel transported?
I didn't say that they cannot be parallel transported, but they are now no longer the same fucking vector. My argument that "Two vectors cannot be neither parallel nor intersecting" doesn't refute the fact that vectors cannot be parallel transported you fucking mongo

A plane is an array of an infinite number of parallel lines

>but they are now no longer the same fucking vector.
Why not? The existence of a plane doesn't magically change the definition of vector to mean it has an inherent position, does it?

>My argument that "Two vectors cannot be neither parallel nor intersecting"
That was my argument though. What are you even trying to say?

Okay thanks for the input, but that has nothing to do with vectors.

>That was my argument though. What are you even trying to say?
Sorry, I meant to say "My argument that 'Two vectors cannot be neither parallel nor intersecting' is bullshit"

>Planes have nothing to do with vectors
Are you even taking linear algebra?

Okay, then I'll ask you again. What bit of linear algebra knowledge am I missing? Why is my claim bullshit?

No, I already took it. But I have yet to see how "two vectors cannot be neither parallel nor intersecting (two vectors cannot be skewed)" follows logically from "planes exist".

>"two vectors cannot be neither parallel nor intersecting (two vectors cannot be skewed)"
This is actually what I'm arguing. What I meant was I have yet to see how the opposite follows logically from "planes exist"

Call me a retard but... don't you mean that two vectors can't be neither paralell nor intersecting in R2?

Your claim is bullshit because you said that there cannot be two vectors that are parallel but not intersecting. How can you not see that this claim is false? I'm done

>don't you mean that two vectors can't be neither paralell nor intersecting in R2
>R2
If that were the case, his claim still wouldn't be true

A,B,C,D points in R^3
M=(A+B)/2
N=(C+D)/2
Want to show
| M-N| < 1/2 ( |A-C| + |B-D|)
i.e.
| (A-C)+(B-D)| < |A-C| + |B-D|
Triangle inequality.

Ah fuck, you're right m8.

>Okay thanks for the input, but that has nothing to do with vectors.
mathworld.wolfram.com/Plane.html
>"A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors"

en.m.wikipedia.org/wiki/Skew_lines

No. I mean that two vectors cannot be parallel nor intersecting. If two vectors are parallel (and share an origin) they will be on the same line and in that sense are intersecting. If two vectors are not parallel, they will still intersect at the origin. In this way I mean that two vectors cannot be neither parallel nor intersecting. If they are parallel, they are intersecting. This is why terms like this are nonsense for vectors.

>Your claim is bullshit because you said that there cannot be two vectors that are parallel but not intersecting.
If we were talking about line segments, you'd be correct. But we're talking about vectors.
No

>en.m.wikipedia.org/wiki/Skew_lines
>Skew_lines
>not Skew_vectors
This is what I'm talking about. You can't just exchange words that have different meanings. None of you know the correct terminology and you should be ashamed of even trying to defend your position with such faulty knowledge. Go reread a linear algebra textbook.

No, actually read it. Don't just read the title. Read the "testing for skew lines" part

Okay. I'll entertain you.
>Testing for skewness
>If each line in a pair of skew lines is defined by two points that it passes through, then these four points must not be coplanar
Already you see, that since any two vectors share a common origin, they are automatically coplanar. You cannot have skew vectors, only skew lines. Don't make me read shit that is trivial.

Vectors intersecting doesn't make any sense.

Lines can intersect. Every line is an infinite set of points. Those points are also vectors since they are elements of a vector space but a set of vectors isn't a vector itself.