Mathematics

smackcrane

12:00 AM

brilliant!

Link

Thanks

Pilot

Hello, I have got a question, what is the dimension of a straight line in 3 D, is it 3 or 0?

Could anyone help me with it please?

smackcrane

a straight line in 3 dimensions? seems like it had ought to be 1 dimensional. what's the context of this question?

Khromonkey

it is 1

linear independence

Pilot

let the intersection of 2 planes(vector spaces) in 3 dimensional space be a straight line,then the dimension of the intersection is 0 and dimension of sum of 2 planes is 3?

Khromonkey

12:13 AM

Take any point on the line

Then take the vector which has head at that line and tail in the origin

Your whole line is the space which has that vector as its basis.

Therefore that vector space has dimension 1

Pilot

what else has dimension 0 except for a point

smackcrane

if we're talking about vector spaces, the only vector space with dimension 0 is $\{0\}$

i.e. the trivial space

user19161

@Pilot A point, line and plane is of dimensions 0,1,2 respectively.

user19161

The dimension of a vector space is the number of elements in a basis.

user19161

Vectors in the basis are linearly independent and span the space.

Pilot

12:29 AM

@Khromonkey the heads of all linear combiantions of that base makes a line?.I am unfamiliar with geometric interpretation sorry but I want to know

user19161

@argon Have you done your HW?

Pilot

I dont get it,but this base different direction

Argon

@WillHunting Sorta.

Studying

user19161

@Argon OK, what are you doing here then?!

Argon

@WillHunting Well, nothing!

Link

12:32 AM

@smackcrane, about earlier why are the equations acceleration both positive? Like it is $.27g = gsin \theta$ and $1.13g = gsin \theta$ Shouldn't .27g be negative if acceleration is up the ramp, and down the ramp is positive?

smackcrane

@Link the accelerations are given in the question, right? I suppose they're just giving you the magnitude, and letting you figure out the directions.

Pilot

@WillHunting doesnt it depend on dimension fo space they are being considered

Link

Yes

smackcrane

@Link it's not a bad idea to set a coordinate system and make sure all the signs are right though

Link

So, it doesn't matter?

user19161

12:36 AM

@Pilot Well, if we have a vector space we can talk about its subspaces, all of which pass through the origin. If you are simply talking about points lines and planes without vector spaces, then there is no dimension to speak of in a way. Of course one can still have that a plane is spanned by two vectors and so on.

user19161

@Pilot Do you know what a vector space is? Have you studied linear algebra in college?

smackcrane

... not as long as the signs agree with each other. but now that I think about it, the accelerations are actually in the same direction. right? it's accelerating down the ramp both on the way up and on the way down

Link

Okay, so if I set up the ramp to be positive, down to be negative: I get: $1.13g=gsin(\theta)-f/m$ and $-0.27=gsin(\theta)+f/m$

is that right?

Pilot

I know abstract concepts

smackcrane

@Link not quite

Link

12:39 AM

Hmm, why is it accelerating down the ramp both ways?

smackcrane

@Link well when it's going up, it velocity is in the positive direction, but it's slowing down, so acceleration is in the negative direction.

and when it's going down, velocity is in the negative direction, and it's speeding up, so acceleration is negative as well

Link

wait what?

Down the ramp is positive, and up is negative..

smackcrane

opposite of what I said, then

Link

So going up the velcoity is negative, and accelration postive

smackcrane

right

Link

12:41 AM

and going down vel is postitive and accel negative

smackcrane

acceleration is positive on the way down, because it's getting faster, so acceleration is in the same direction as velocity

Link

but the question said going down the ramp the accelration is .27g up the ramp

shouldn't accel be negative then?

smackcrane

if the acceleration is indeed .27 up the ramp, then acceleration would be negative ... and that would change things, because we'd have different signs on some stuff

Link

It is

then how would the equations be then?

smackcrane

cool. so up the ramp is our negative direction, and down the ramp is our positive direction ...

Link

12:46 AM

yup

smackcrane

acceleration on the way up is 1.13g down the ramp right? so that's +1.13g on the left hand side

and the components are $g \sin(\theta)$ gravity pulling down the ramp, and $f/m$ friction pulling down the ramp. both positive

Link