Parametric Definition and 674 Threads

How can I find the parametric vector form of a cartesian equation under a specific condition? Cartestian equation: $$-2x-y+z=6$$ I know to find the parametric vector form we can find any 3 points P, Q and R which satisfy the cartesian equation. $$ \begin{pmatrix} x_1\\ y_1\\ z_1...

Homework Statement Sketch the trajectory over the time interval 0 ≤ t ≤ 10 of the particle whose parametric equations of motion are given by X= t−3sint . And y = 4 − 3cost find the value of x,y,t Remember that you should be in Radian mode! Answer Do you isolate the t first and plug it in...

Homework Statement [/B] Show that the given parametric curve decribed by the following notations: x=cos(t), y=sin(t), z=2+2cos(t) lies in a single plane ,find the normal vector to this plane Homework Equations --- [/B] r(t)=cos(t) i + sin(t) j + 2+2cos(t) k The Attempt at a Solution My...

Homework Statement Find parametric equations for the portion of the cylinder x2 + y2 = 5 that extends between the planes z = 0 and z=1. Homework Equations I can't really find any connection but I do have x=a*sinv*cosu y=a*sinv*sinu z=a*cosv The Attempt at a Solution I...

Hi everybody, i just joined. Here's my first post I have a few questions. When looking at curve C and by the eye test, it doesn't pass the VLT, even though x=f (t ) and y=g (t) are functions,...then overall with curve C not passing the VLT, is it still a function since f (t) and g (t) are? I...

Homework Statement I want to know if I got the answer correct and if my reasoning is sound. The text answers and solutions manual only gives answers/solutions for odd numbered problems. Here is the problem: And a direct link to the imgur page: http://i.imgur.com/Tko1xFh.png Homework...

Homework Statement Sorry to disappoint the math fanatics but no this is not a question that integrates all three topics at once but individual ones. I still need assistance though with the following more so in the reasoning behind them as I feel my logic is flawed...

Homework Statement Why does \int_a^b \, y \; dx become \int_\alpha^\beta \, g(t) f^\prime(t) \; dt if x = f(t) and y = g(t) and alpha <= t <= beta? Homework Equations Substitution rule?The Attempt at a Solution I'm not sure how y = y(x) in the integrand turns into g(t). Isn't y a...

Homework Statement (a) Show the curie-weiss behaviour. (b) Estimate ##\lambda## and ##B_e## and exchange energy.[/B] Homework EquationsThe Attempt at a Solution Part(a) Since even when applied field is zero, ##B_{total} \neq 0## which gives rise to ##M\neq 0##. This is a fundamental...

Homework Statement Let C be the straight line from the point r =^i to the point r = 2j - k Find a parametric form for C. And calculate the line integrals ∫cV*dr and ∫c*v x dr where v = xi-yk. and is a vector field Homework EquationsThe Attempt at a Solution For parametric form (1-t)i + (2*t)j...

How we can know the parametric equation for any curve? Is there some trick? Like for parabola ## y^2 =4a x ## It has general coordinates## (at^2 , 2at) ## It will satisfy the equation but how in first place we know it? Also we can have ##(a/t^2, -2a/t) ##, how?

Homework Statement Find the area under one arch of the cycloid x=a(t-sint), y=a(1-cost) Where do I start? I could divide both sides by a and get x/a= t-sint cost=1-y/a If this is the case, how should I deal with x/a=t-sint? I need to get them into the form of sint=... or cost=... right?

Homework Statement I am trying to find parametric representation of the right surface of a sphere which was cut along the line y=5. x^2 + y^2 + z^2 = 36 Homework EquationsThe Attempt at a Solution x^2 + y^2 + z^2 = 36 This is an equation of a sphere with radius given by: r^2 = 36 r=6...

Hi, I'm majoring in fluid mechanics. I notice some researchers are using the phrase parametric instability. I googled it, it seems this comes from the solid mechanics (vibration). Can you explain to me what's the difference between parametric instability and the resonance? They seem the same...

This might seem like a naive question to ask, but a full explanation of why these two concepts are different would be welcome. I am confused because parametric equations are ##y = 8t^2## and ##x = 5t##, but at the same time, these two equations can describe the ##x## and ##y## components of a...

Homework Statement Find all the points on the following curves that have the given slope: x=4cost y=4sint slope=1/2 Homework EquationsThe Attempt at a Solution Im not to sure what to do with this question.. I found dy/dx to be -cot(t) but I am not sure if that is even needed for this...

Homework Statement "Let L1 be the line having parametric equations : x = 2 - s, y = -1 + 2s, z = 1+s and L2 be the line: x = 1 +t, y = 2+ t, z =2t . a. Do the lines intersect? If so, find the point of intersection. b. Find the point P on the graph of L1 that is closest to the graph of L2...

I am trying to make sense of these articles http://info.kubotek3d.com/3D-Engineering-Software-Tools-Kubotek-Blog/?Tag=Direct%20CAD%20vs%20Parametric%20CAD and http://en.wikipedia.org/wiki/Explicit_modeling . To me this sounds like "if using parametric relations is too complex, let's stop using...

I am studying differential geometry of surfaces. I am trying to understand some features of the first fundamental form. The first fundamental form is given by ds2 = αijdxidxj Now if the αijs are all constants (not functions of your variables) then I think (correct me if I'm wrong) that the...

hi, I'm currently really struggling with an assignment that I've been tasked with. https://ss1002.files.wordpress.com/2015/01/assignment.pdf It's mostly theoretical proof questions, which I find difficult. Actual questions I'm fine with. I have done the first question without issue, as...

Homework Statement The line L L1: x=3+2t, y=2t, z=t Intersects the plane x+3y-z=-4 at a point P. Find a set of parametric equations for the line in the same plane that goes through P and is perpendicular to L. Homework Equations cross-product r=r0+t(vector) this is to get in parametric form...

$\textbf{Problem}$ Given $\textbf{v} \ne \textbf{0}$ and $\textbf{p}$ in $\mathbb{R}^n$, the line through $\textbf{p}$ in the direction of $\textbf{v}$ is given by $\textbf{x} = \textbf{p} + t\textbf{v}$. Show that linear transformation $T: \mathbb{R}^n \rightarrow \mathbb{R}^n$ maps this line...

Hi everyone. On these days, by watching solar panels and similar stuff, I just thought about it, and why they take such a wide surface to produce energy, and why their output is often low, as we all know. By navigating here on the internet, I've just seen a device called OPO (Optical...

For the parametric equations x = t^3 - 3t and y = t^3 - 3t^2 I got that the graph has a vertical tangent when t is = to postive or negative one. And it is horizontal at t = 2. However, this implies that at the point (x,y) = (2, -4) the graph has both a vertical and horizontal tangent. How...

(This is actually a calculus problem, not a physics one, but physics is based on calculus, so I hope it's fine) 1. Homework Statement Eliminate the parameter to find the Cartesian equation of x = (1/2)cos(θ) y = 2sin(θ) Homework Equations x^2 + y^2 = 1 (eq of circle) The Attempt...

Hello. Let's imagine that we have a parametric function f1(x(t),y(t),z(t)) and an analytic one f2(x,y,z) and we have to integrate their product over some volume dx dy dz. So what are analytical tools for it? Thanks!

So I was watching this video on Khan Academy, and it talks about graphing functions that have values in multiple dimensions. It shows how to represent a linear function in 3 dimensions with a set of vectors, L ={p1 + t(p1-p2)|t∈R} where p1 and p2 are vectors that lie on the line you want to...

I have a doubt in 3d geometry. I calculus and I know how to do partial derivatives.(but I don't know what it means). If you have a parametric equation ##x=t, y=t^2,z=t^3## (the equation is randomn) What does ##\vec{r}=t\hat{i}+t^2\hat{j}+t^3\hat{k}## represent? now if it represents the position...

Homework Statement Let C be the curve given parametrically by x = (t^3) - 3t; y = (t^2) - 5t a) Find an equation for the line tangent to C at the point corresponding to t = 4 b) Determine the values of t where the tangent line is horizontal or vertical. Homework Equations dy/dx =...

Hello everyone, I have another question mark buzzing inside my head. After the elimination steps of a matrix, I'm having some problems about imagining in 3D. For example, x=t , y=2t, z=3t what it shows us? Or, x=t+2, y=t,,z=t ? Or another examples you can think of. ( Complicated ones of...

Hello PF, I've got a curiosity question someone may be able to indulge me on: The set of implicit functions covers a certain function-space - the set of all functions that can be represented by an implicit relation. Parametric functions also covers a function-space, that at least overlaps...

Homework Statement [/B] You are given a particle, with the trajectory of a circle, with radius of 3 meters. The particle moves clock-wise, and when t=0, the x, y coordinates are (0, -3). Find parametric equations for the coordinates (x, y) in terms of the parametric t (time). Homework...

Homework Statement Homework EquationsThe Attempt at a Solution For part A) my answer was:[/B] \int_a^b \sqrt{(dx/dt)^2+(dy/dt)^2}dt The work I used for part A was based off this sites explanation: http://tutorial.math.lamar.edu/Classes/CalcII/ParaArcLength.aspx For part B) I simple took...

Homework Statement I am given a line that passes through the points (x0, y0, z0) and (x`,y`,z`) and a plane in 3D space being defined by these three nonlinear points (x1, y1, z1), (x2, y2, z2), (x3, y3, z3). Im directed to use cramers rule to find the intersection of the line and plane...

Hi everyone! I'm having some issues with this problem for linear algebra. I understand parametric equations fairly but I'm confused about the unit vector notation 1) Consider the plane r(s,t)=2i + (t-s) j + (1+3s-5t) k find the z component of the point (2,-1, z0) For what values of s and t is...

Homework Statement Hi, so confused abou this question that I probably haven't even posted it in the correct section.Here's the question. A wheel of radius ,r, is situated at the top of a ramp having an angle θ = π/6 rad. At t= 0 the wheel is at rest with its centre at coordinates (0,r) and...

Homework Statement Consider the curve with parametric equations: x = t - cos t, y = sin t. Determine exactly the equation of the tangent to the curve at the point where t=-0.5pi. Homework EquationsThe Attempt at a Solution The equation of a line is y - y1 = m ( x - x1 ) I substituted t = -pi/2...

Homework Statement Eliminate the parameter to find a description of the following circles or circular arc's in terms of x and y and find the center and radius and indicate the positive orientation x=cos(t) , y = 3sin(t) ; 0< t < pi/2 (should be less than or equal to) Homework Equations Not...

I would like some help understanding some parts of spontaneous parametric down conversion (SPDC).In the Wikipedia article on the topic…http://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion…the third figure from the top is labeled “An SPDC scheme with the Type II output”. The figure...

1. Write down the equation for the line in 3D through the point a=(1,2,4), parallel to the line r=(1,-5,0)+λ(1,2,2). Then, find the distance between these lines. 2. 3. Lets say, b= (1,2,2). b is parallel to given line, so it must also be parallel to the new line. My guess is that the equation...

Homework Statement I have this equation and i need to find the cartesian equation, so i apreciate your help Homework Equations X=cost ' y=2sin2t The Attempt at a Solution I am usign this [/B] Sin2t=2costsint So x+y/2=cost+2costsint But i don't know what to do after, I also try to solve that...

Hello! (Wave) What is Parametric Statistics about? (Thinking) What knowledge is required? Is it difficult? (Worried) Would you suggest me to take Parametric Statistics or Stochastic Processes? :confused:

i graphed the parametric equations x=t y=t^2 and z=2 on my nspire in 3d and it came out looking like this (Blush) i have made them pretty so you can see the graph properly anyways what my question is, is that ( :confused: "is is" ) is the graph supposed to look like that? on a 3d plane? did...

Homework Statement Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Homework Equations x = 1+2 \sqrt{t}, \quad y = t^3 - t, \quad z = t^3 + t, \quad (3, 0, 2) The Attempt at a Solution I began by...

Hi, so after doing some calculus for projectile motion with air resistance, I obtained two equations of vx(t) and vy(t) that describes the vertical and horizontal motion of the projectile. Please tell me if I'm wrong, but I believe since both vx and vy are functions of t, can't they be...

Homework Statement Find a parametric form for the part-cubic curve with equation y = x3, 0 ≤ y ≤ 8; starting point (2, 8), The Attempt at a Solution The question beforehand was the exact same but the starting and ending points reversed. My answer for that was; r(t) = (t, t^3) for t an...

match the parametric equations with the graphs. i need help with 21 23 and 25. i have the answers but i need explanations for why that specific graph matches with the set of equations. I've been stuck on these for a long time. please help!

Find vector and parametric equations for the segment that joins the points p(2,0,0) and q(6,2,-2). The examples in my book make no sense and i don't understand cheggs method. I know that r=(1-t)r_0 + t*r_1. I only need help finding the vector equation. Can someone give a step by step explanation?

Hey Everyone! I have three questions that I do not know how to approach/solve. I've been checking online, the textbook, etc, and nothing. This is Calculus 2.1. Find the points with the given slope. x=9cos(theta), y=9sin(theta), slope = 1/2. Answer: (-9rt5/5, 18rt5/5), (9rt5/5, -18rt5/5)...

eliminate the parameter to find a cartesian equation of the curve. $x=sin\frac{1}{2} \theta$ $y=cos\frac{1}{2} \theta$ $-\pi \le \theta \le \pi$ $x=e^t-1$ $y=e^{2t}$