3 dimensions Definition and 68 Threads

Homework Statement http://carlodm.com/calc/123.png My question is: Why can't we use a scalar multiple like (3/8) PQ instead of using the midpoint formula twice (to get 3/8) ?

Is it possible to change: _______ distance = \/X2 + Y2 To: _______________ distance = \/X^2 + Y^2 + Z^2 And get the distance between a point in 3 dimensional space and a the point of origin, just as the first equation does in 2 dimensional space...

Homework Statement A sphere of radius r and mass m rolls without slipping inside a hollow cylinder of radius R. z direction goes along axis of cylinder. Determine the Lagrangian with motion in the z direction included Homework Equations I let θ be the angle of the sphere rotation...

I have an equation for a curve that lies along the surface of a truncated cone. In polar coordinates: theta(r) = K * [ U + arctan(1/U) - (Pi/2) ] where: U = SQRT[ ((r/r1)^2) - 1 ] K = SQRT[ 1 + (H/(r2-r1))^2 ] r = r1 + (r2-r1)(z/H) r1 = minor radius of the truncated cone r2 =...

Homework Statement Evaluate: \int _C{xydx - yzdy + xzdz} C: \vec{r}(t) = t\vec{i} + t^2\vec{j} + t^4\vec{k} o <= t <= 1 Homework Equations The Attempt at a Solution I understand that you cannot use Green's Theorem in 3 dimensions. How else can I go about solving this?

Homework Statement Homework Equations Fe = (kq1q2)/r^2 The Attempt at a Solution So for part A and B what is the best way to go about doing this? Could I find the distance between the charges and just use coulombs formula?

This is my last annoying post here, probably. :) Homework Statement I have a curve \alpha: I \rightarrow \Re^3 parametrized by arclength. \kappa(t) \neq 0 for all I. Given the surface \psi (s,t) = \alpha (t) + (s-t) v(t), where v(t) = \frac{d \alpha}{dt}, t is in I, and s > t, I want to...

1. Variables Given a generalized basis in three dimensions: e_{1},e_{2},e_{3} and the standard Kronecker delta \delta_{ij}, and using Einstein summation. With the vector \textbf{x},\textbf{y},\textbf{z} I'm trying to simplify this problem: 2. Problem \delta_{il} . \delta_{jm} . x_{j} 3. My...

http://folk.ntnu.no/stoylen/strainrate/mathemathics/ This page shows how to find shear strain in three dimensions. I understand how they found the shear strains as x and y components from dividing the change in length by the original length. But from the line "From the figure, it is...

Homework Statement A train at a constant 79.0 km/h moves east for 25 min, then in a direction 37.0° east of due north for 18.0 min, and then west for 54.0 min. What are the (a) magnitude (in km/h) and (b) angle (relative to north, with east of north positive and west of north negative) of its...

Given F = (-20i + 50j = 10k) 1. The component of the foce projected along the pole AO. 2. The magnitude of the projected component of the F along the pole AO. I have no idea where to begin, I think I need to find the angles but I'm not sure how in three dimensions. (please excuse...

Homework Statement Two lines in space are in the same plane. Line AB passes through points A(x,y,z) and B(x,y,z), and line CD passes through points C(x,y,z) and D(x,y,z). Determine if these two lines are parallel. If they are not, determine the x,y,z coordinates where these two lines...

What do electromagnetic waves look like in 3 dimensions? In my textbooks etc. they are always represented as the standard sine wave. But what about actual 3 dimensions? Are there waves with smaller wavelengths than gamma waves?

Hello everyone! I'm confused on what I'm suppose to do here, I think i might got it though but i need to make sure... Here is the problem and my work: http://show.imagehosting.us/show/764032/0/nouser_764/T0_-1_764032.jpg he let r(t) = f(t) i + g(t) j + h(t) k. So if i multiply this by...

i am attempting to find a solution for the n-body problem, but i don't know the equations for gravity in three dimensions. if someone could post them for me, i would be most appreciative. thank you also, any advice as to how to approach this problem would be appreciated as well

I am not sure how to form a coherent question about this; I can't figure out how to phrase it: Why are our three dimensions all at 90 degrees to each other? Drat, I can't even form the question. I've been reading about extra dimensions, such as the further 6 postulated in string theory...

i understand the concept of dimensions until we get to 3 but having more than 3 dimensions is beyond me. anyone care to explain? thanks.

I'm confused about what people mean by 5,6,7, and 11 dimensions. Are they referring to spatial dimension? Are they referring to different dimensions like time is a "dimension" in addition to space? If we're talking about spatial dimensions, how can you have more than 3? Spatial...