Plane Definition and 1000 Threads

Homework Statement Let A, B and C be distinct vectors in V3 with B and C non-parallel. a. Find an equation for the plane containing both the line through A parallel to B and the line through A parallel to C. b. Verify that the two lines actually lie in the plane. Homework EquationsThe Attempt...

How can we calculate the slipping of an object down an inclined plane?

Homework Statement Plane harmonic waves of 1/p, 1/q, 1/r and 1/s are travelling, respectively, in the directions of the (non-unit) vectors (1,1,1), (1,-1,-1), (-1,1,-1) and (-1,-1,1). Show that there exists an inertial coordinate system in which they have the same frequency if and only if...

Say that I have two vectors that define a plane. How do I show that a third vector is perpendicular to this plane? Do I use the cross product somehow?

Homework Statement What is the distance from the point P to the plane S? Homework Equations ## S = \left \{ r_{0} + s(u_{1},u_{2},u_{3})+t(v_{1},v_{2},v_{3}) | s,t \in \mathbb{R} \right \} ## The Attempt at a Solution [/B] I found an expression for the general distance between point P and a...

Homework Statement Homework Equations none The Attempt at a Solution Two possible locations on the coordinate axis for the terminal arm of angle A: Two possible values for the measure of angle A and the related acute angle: Can someone please tell me if I did this correctly?

Hi everyone. I am told to find the equation of the tangent plane to the surface x^2 + 2xy^2 -3z^3 = 6. I do not know how to approach this problem, and I was wondering if anyone would be kind enough to help. I know that for example if I had an equation z = x^2 + y^2, with a point P(x0,y0) and...

A very clever first-year physics student I know, who had just been learning about the Doppler effect, asked me a question. If a plane were flying a straight trajectory at Mach 2, playing a song on its speakers very loudly, and an observer with incredibly sensitive recording equipment were to...

Homework Statement The signboard truss is designed to support a horizontal wind load of 800 lb. If the resultant of this load passes through point C, calculate the forces in members BG and BF. [/B]Homework Equations For a solution using the method of sections for plane trusses,any three...

Hi, I'm currently reading Calc III by Marsden & Weinstein. One of the examples shows a plane being drawn through three points. While I understand their solutiom, I'm very curious as to why my solutiom doesn't work. 1. Homework Statement Write the equatiom for a plane through A = (1, 1, 1), B...

1) If the angle of incidence of a ray of light to mirror is 50 degrees, what is the angle of reflection from the mirror? 2) If the angle of incidence of a ray of light to a mirror is 20 degrees, what angle does the light ray make with the mirror when it reflects? 3) If a ray of light makes an...

Homework Statement I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently...

Projective Algebraic Geometry - the Projective Plane ... Cox et al - Section 8.1, Exs 5(a) & 5(b) I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra...

Homework Statement The wheel shown rotates about point O. Point A has a velocity=-7j in/sec. Point B has a tangential velocity=-4i in/sec^2 Determine the absolute acceleration of Point C located on the circle. radius=6 in You will have to look at the figure for more clarification please...

Homework Statement I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently...

I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused on...

I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused on...

This is not a homework question. School year has ended for me and I'm doing some revision on my own. I want to proof the following because in an exercise I had to find the equation of the line that passed through a given point and 2 given lines. If a line r intersects with 2 given crossing...

I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused on Chapter...

I am reading the undergraduate introduction to algebraic geometry entitled "Ideals, Varieties and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra (Third Edition) by David Cox, John Little and Donal O'Shea ... ... I am currently focused on Chapter 8...

A 10 Kg block lies on a smooth plane inclined at 51 degrees. What force parallel to the incline would prevent the block from slipping?

Why are the blades of air plane propellers thin compared to ship propellers? Why shouldn't air planes use the same blade design?

Homework Statement This problem asks for the angle on an inclined plane-- I have attached the problem below. Homework Equations fnet=ma The Attempt at a Solution I honestly have no idea what to do. I found the vector components for gravity and made a FBD for the box, but I can't really figure...

Homework Statement These two problems are inclined plane problems which I cannot figure out. The problems are attached in the image below. Homework Equations Fnet=ma The Attempt at a Solution I first broke down the gravity force into its x and y components. After that, I did this...

Hi all, This is from a past exam paper: At t=0 the state of a particle is described by the wavefunction $$ \Psi (x,0) =A(iexp(ikx)+2exp(-ikx)) $$ This is between positive and negative infinity - not in a potential well. What values of momentum are allowed, and with what probability in each...

I've been looking for a simple exact, gravitational plane wave solution. Working from Wiki's short article on Brinkmann coordinates, I have what appears to be a simple exact solution - but it's significance and interpretation is confusing me a bit. Let's start with the metric: $$g = (y^2 -...

Homework Statement A projectile is thrown at angle θ with an inclined plane of inclination 45o . Find θ if projectile strikes the inclined the plane horizontal Homework Equations Taking x-axis along the incline and y-axis perpendicular to incline.[/B] Vx=ucosθ - gsint(45)t Vy=usinθ -...

Homework Statement An object is on a frictionless inclined plane. The plane is at an angle of 30 degrees with the horizontal. What is the object's acceleration? a) 0.50g b) 0.56g c)0.68g d)1.0g e)0.87g Homework Equations F=ma a = g.sin(theta) The Attempt at a Solution I set it up where...

Homework Statement Homework Equations W_g = mgdcos(phi) The Attempt at a Solution So the angle between the force doing work (x component of F_g) and the displacement (down the hill) is 0 degrees. aka phi is 0 degrees. This is true for (a), (b) and (c). so since cos(0) = 1, the work done by...

I am having a difficult time seeing the three dimensional surface formed from a plane of equation 2x + y + z = 2 strictly inside the first quadrant. On the 2 dimensional xy plane, the closed, simple, piece wise curve is C1 along the x-axis from x=0 to 1, C2 along the line y= 2-2x is between...

Homework Statement [/B] Homework EquationsThe Attempt at a Solution Honestly speaking , I have little idea about this problem . All I can think of is that since the particle is in static equilibrium , the particle has no acceleration . So , if T is the tension in the string then resolving...

Hi again. I hope this is the right section to ask this question. Not home work (I'm retired) but yet another mind game I'm playing (and still getting nowhere). I have trying to work out the formula for how a ski will perform a carved turn. I have looked at many (many Many) websites and they...

A plane mirror forms a virtual image of a real object placed in front of it and a real image of a virtual object placed in front of it. I can't picture the second case. Please show me a ray diagram showing real image formation by a plane mirror or just explain the case of real image formation by...

Homework Statement Homework EquationsThe Attempt at a Solution To bring the cylinder to a stop both linear impulse and angular impulse would be required . Linear impulse would be provided by the normal force from the plane whereas the angular impulse has to be provided by the frictional...

Homework Statement Sorry for the dull question. Problem is as shown/attached Homework Equations The waves in part ii) are traveling in a HIL dielectric of permittivity ##\epsilon_{r}## from ##0 <z<d## and then hit an ideal metal boundary at ##z=d##. The Attempt at a Solution I figure this...

I found this clip on youtube of a plane getting pushed on ice due to strong winds. Have a look. I guess I just want to hear some comments about what is reallly going on here. How we can estimate the force of the wind pushing, what chance the ramp agent has of holding the place himself if say...

Hi, as we know all objects must be three dimensional. If there is two dimensional "object" or "shape" in the universe, "it" will not look different from space or nothing as "it" is neither thick nor thin. Mathematicians calling "it" as a "surface" but "it" have zero thickness, isn't it a...

So I know that a complex number can be represented by ##z=x+iy##, where ## z = x + iy \in \mathbb{C}##. Would it be okay to then state that ## z = x + iy \in \mathbb{C} := (x,y) \in \mathbb{R}^2 ##? If we can just look at complex numbers as coordinates in ##\mathbb{R}^2## what is the point of...

A passenger plane is traveling at a speed of 500 knots, has a mass of 72574.7792 kg, and has an altitude of 35,000 feet. If the pilot lost control of the plane and couldn't reduce speed or anything and the plane was going down at approximately a 40 degree angle, how long would you have until it...

This is way too stupid to make up: https://www.washingtonpost.com/news/rampage/wp/2016/05/07/ivy-league-economist-interrogated-for-doing-math-on-american-airlines-flight/ Zz.

Homework Statement The method that we are taught on how to determine the equation of a plane is as follows when given 3 coplanar points: 1. Determine the vectors 2. Find the cross product of the two vectors. 3. Substitute one point into the Cartesian equation to solve for d.Homework...

Homework Statement If W is represented as the point shown in blue which of the other points satisfy z=Sqrt[w]? Homework Equations The Attempt at a Solution (The answer is Z2)[/B] I'm trying to study for a test and this is a practice problem and the book doesn't go into great detail about...

Note:- All surfaces given here are frictionless. To find:- Acceleration a Relevant eqs:- F = ma Attempt at solution:- The equations I've gotten so far:- 1) N1sin(theta) = m2a 2) m1gsin(theta) = m1a1 3) m1gcos(theta) - N1 = m1a2 So far, 3 eqs, 4 unknowns. For the 4th eq, I did a2sin(theta) =...

I'm not sure if I should be posting here of all places but it's worth a shot. I just had my unit test and there was a pretty weird problem on it where there was a circle of radius r in 3space on the plane of ax+by+cz=d and you were given the circle's center (C1,C2,C3). To be clear, I was given...

I've been thinking about the flat surface we call a plane. I've looked for definitions and none of the ones I have found satisfy me...in this respect...they seem dependent on assumed meanings and not self-dependent using only geometric contructions. Let me explain. One definition of a plane...

Homework Statement The cylinder x^2 + y^2 = 1 intersects the plane x + z = 1 in an ellipse. Find the point on the ellipse furthest from the origin. Homework Equations $f(x) = x^2 + y^2 + z^2$ $h(x) = x^2 + y^2 = 1$ $g(x) = x + z = 1$ The Attempt at a Solution $\langle 2x, 2y, 2z \rangle...

Homework Statement In the "Before" scenario, there is conductive plate in electrostatic equilibrium with uniform surface charge density +η (the plate has some thickness but the width and length are significantly larger). In the "After" scenario, an infinite plane of negative charge with fixed...

Homework Statement Hi ! :) I'm having some difficulties with the question below, in which there are numerous steps and I am unsure in which part(/s!) I have gone wrong. The question is as below; you must via integration calculate the shaded volume of a perfect cylinder of radius R and height...

Not exactly homework in my case but I guess it fits the level. We know that a = v dv/dx holds when moving on a line. Does it hold when moving on a plane? If yes, what would be the exact formulation of the statement. I mean, I read a = v dv/dx as a(x) = v(x) dv/dx(x) (or are they functions of...

Homework Statement So I am trying to accomplish the above by using spherical coordinates, I am aware the problem may be solved using dv=dxdydz= zdxdy were z is known but I would like to try it using a different approach (using spherical coordinates). Any help would be greatly appreciated...