Planes Definition and 523 Threads

Homework Statement Equation of the plane Containing the line r(t) = <2 − t, 3, 4 + 2t> and point P(0, 0, 1). Homework Equations ax+by+cz=d equation of a plane The Attempt at a Solution 1) We have a point, we need a normal vector 2) this time we are giving a line ON the plane, so the...

Homework Statement Find an equation to the plane: 1)Orthogonal to the line r = <t, 2 − 3t, 4> and passing through the origin. Homework Equations Equation for a plane: a(x-xi)+b(y-yi)+c(z-zi)=d The Attempt at a Solution Okay, so this is really a matter of 'slope' and understanding the values...

Homework Statement Find an equation of the sphere with center (2, -6, 4) and radius 5. Describe its intersection with the each of the coordinate planes. Homework Equations Equation of a sphere with three dimensions X2 + Y2 + Z2 = R2 The Attempt at a Solution My equation is (x - 2)2 + (y +...

There are several sites on the web that pose a physics problem that states that "the Russians" sometimes dropped soliders from planes into the snow without parachutes. (e.g. on physicsforums we have: https://www.physicsforums.com/threads/parachuting-inside-bales-of-hay.792412/ ) Is this a...

Homework Statement Find a set of parametric equations for the line of intersection of the planes. 6x-3y+z=5 and -x+y+5z=5[/B]Homework Equations The cross product formula The formula for the parametric equations of a line in three dimensional space: x=x1+at, y=y1+bt, z=z1+ct Knowing the fact...

Homework Statement I am preparing for my calculus III class over the break. I came across the formula for the angle between two planes which is: cosΘ = (|a.b|)/(||a|||b||) Homework Equations cosΘ = (|a.b|)/(||a|||b||) a.b = ||a||||b||cosΘ The Attempt at a Solution I know that the dot product...

Homework Statement Hi, An equation of the form Ax + By + C = 0 is a standard equation of a line in 2D. An equation of the form Ax + By + Cz + D = 0 is an equation of a plane. Is it possible to: Describe a plane in space, written in standard form, such that one variable is missing from the...

According to my book, if we write the equation of a plane as: ##ax + by + cz = d## And two planes have values of ##d## with the same sign, they are on the same side of the origin. If they have values of ##d## with different signs, they are on opposite sides of the origin. I'm confused as to...

what is definition of closed packing?a close packing plane is a plane that the atoms cannot be packed any closer?

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 An m1 = 7.6 kg block and an m2 = 10.7 kg block, connected by a rope that passes over a frictionless peg, slide on frictionless incline. Find acceleration of boxes and tension of the rope. Homework Equations F=ma I'm not sure what else The Attempt at a Solution I'm really...

Hi Guys Recently I have started a new hobby into RC planes. What I have noticed is extensive use of Carbon composites weight yet sturdy structures. Now the problem is that these structures seem to be cut (milling/drilling/laser cutting/water jet cutting) from a sheet (or laminates) of carbon...

Homework Statement Find the equations of the tangent line, normal plane and osculating plane to the curve r(t) = -2sin(t) i + 2cos(t) j + 3 k at the point corresponding to t = π/4. Homework Equations T[/B]^(t) = r'(t) // ||r'(t)|| u = a i + b j + c k, ||u|| = √(a^2 + b^2 + c^2) N^(t) =...

Hi, I was doing a L.A question and a question arose. ( well I will write the question now, I found the answer I just can't visualize what I am doing which bothers me greatly) Find the equation of the plane that contains the line (x,y,z)=(1,0,0)+t(1,3,2), and is parallel to the line of...

For example, given two planes: P1: 3x + y -2z = 4 P2: x + 2y + z = 1 There is a line of intersection between them. The direction vector can be solved by doing the cross product of the two normal vectors for each plane, but then a point must be included to find the exact equation for the line...

Hi! I'm having trouble with this question, any help would be much appreciated! :) Q1: Given the three vectors: n1 = (1, 2, 3) n2 = (3, 2, 1) n3 = (1, −2, −5) Find the intersection of the three planes ni*x = 0. What happens if n3 = (1, −2, −4)? Why is this different?

I have attached an image... Okay, so I have been stuck on this problem for like 2 hours now and I have no idea how to find r(x). I know the trace is the intersection of the plane and the surface. My first attempt was to substitute the plane y+2x=0 equation for the surface equation by solving...

(The degrees is 35.8) So far I thought that i'd solve it like this: Weight of block W = mg Component of W parallel to slope = Wsinθ Component of W perpendicular to slope = Wcosθ Call R the normal reaction force of the slope on the block. In the direction perpendicular to the slope, the...

Let u=<5,-2,3> and v=<-2,1,4>. Find the value of c which will force the vector w=<2c,3,c-1> to lie in the plane of u and v. I did the cross product of u and v, then i crossed u and w, then I equal the product of u and v with what I got for w. But for some reason when I try doing the triple...

Homework Statement Hi I require to compute the volume of a ellipsoid that is bounded by two planes. The first horizontal (xy) plane is cutting directly along the mid-section of the ellipsoid. The second horizontal plane is at a z = h below the first horizontal plane. The volume of the...

Must double integrate using type I or type II planar region D to find volume bounded by Cylinder y^2+z^2=4 And Planes X=2y X=0 Z=0

I'm writing a little bit of Mathematica code that should be able to make a reasonable powder diffraction spectrum. The algorithm is like this: Take Bravais lattice and basis. Compute reciprocal vectors. Compute structure factor (and its square magnitude) Have triple nested loop that creates...

Suppose a force F is acting downwards on an object sitting on a plane that is inclined 45 degrees to horizontal. express the force as a sum of a force acting parallel to the plane and on acting perpendicular to the plane I figured I need to use ||F||cos 45i+ ||F||sin 45j and the...

equations of planes and the meaning of the "d" value Homework Statement Find the equations of the following plane Through (2, 0, 2), (0, 1, 2) and (2, 1, -1) Homework Equations standard form of equation of a plane: ax + by + cz = d The Attempt at a Solution hello I'm trying...

I am reading James Munkres' book, Elements of Algebraic Topology. Theorem 6.5 on page 39 concerns the homology groups of the connected sum of two projected planes. Munkres demonstrates the following: H_1 ( P^2 \# P^2 ) \simeq \mathbb{Z} \oplus \mathbb{Z} / 2 ... ... ... (1) and H_2 ( P^2...

Hi guys, Question is: Find the slopes of the curves of intersection of surface z = f(x,y) with the planes perpendicular to the x-axis and y-axis respectively at the given point. z = 2x2y ...at (1,1). fx(x,y) = 4xy ∴ Slope = 4 fy(x,y) = 2x2 ∴ Slope = 2 Is this wrong? Answer...

Hi, I am trying to follow an introductory problem in my book for which no solutions are provided and have got stuck. I was wondering whether anyone could tell me how to go about this problem and where I am going wrong. The problem starts: Consider the eqquations: y_1= x_1+2x_2...

Homework Statement Determine for what value/s of the parameter a the following planes in R3 are perpendicular: ax + 0y - 5z = 3 ax + ay + 5z = -26 Write answer in form {a,b} or {a} Homework Equations I know that in R2 two vectors are perpendicular if u*v = 0 What what do I use for...

Homework Statement Find equation of plan H in R^4 that contains the point P= (2,-1,10,6) and is parallel to plain H2: 4a +4b + 5c-6d = 3 then answer the following questions: A. find normalized normal of plane H which has an angle theta with the normal n= (4,4,5,-6) of H2 such that...

I'm not sure if this belongs in Astronomy or Astrophysics. Todays APOD featured the rotation of the sun about its own axis. It seems to me that the axis of rotation of the sun should be aligned with the axis of rotation of the plane of rotation of the planets, i.e. the ecliptic, or more...

Homework Statement There are three parallel identical planes of area A = 200 cm^2, and the distance between the upper and the middle one as well as the distance between the middle and the lower one is d = 3cm. The upper plane was charged to q1 = 0.5 nC. The other two were connected to a V=...

I hope I am able to formulate this question properly as I am not extremely versed in differential geometry. I have an arbitrary 3d smooth surface, S, defined by discrete points and their respective normal, N. I also have an arbitrary vector, V, pointing at that surface. I need the min and...

Homework Statement Okay, So I Have A Physics Packet That My Teacher Handed Out On Inclined Planes. I Was Not There So I Do Not Know How To Complete The Table. I Have To Complete A Chart. The Chart Gives Me The Length Of The Incline, The Height, & The M.A. . I Know How To Calculate The M.A...

Hey. I am wondering how can blue and green colour planes exist in a photo, when I am using red bandpass filter while taking photos? Red bandpass filter let's only red light through. But when i analyze the photo, green and blue planes are still there. How can it be? Thanks in advance

Homework Statement It asks to find the volume of the solid given these planes: z = x y = x x + y = 2 z = 0 It also asks to find the volume using 2 iterated integrals with different orders of x and y integration. Homework Equations The Attempt at a Solution I found...

Homework Statement Find the points on the surface \(4 x^2 + 2 y^2 + 4 z^2 = 1\) at which the tangent plane is parallel to the plane \(4 x - 3 y - 2 z = 0\). Homework Equations Not sure The Attempt at a Solution What I did was take the gradient of both functions, the surface...

Hey! I just joined the forum, but would like to get some help with 2D&3D vectors and dot product. I missed some classes due to a bad illness and now can't get the hang of it at all.. Would appreciate it alot, if someone could explain me how to solve these 5 exercises.

Homework Statement Homework Equations The Attempt at a Solution With this problem and in general, I am having difficulties knowing what should be the cubic and what shouldn't be from visual inspection, so in this case I can't tell why I_x is 1/12ba^3, as opposed to 1/12ab^3. How can I tell...

The graph of z=x^2+y^2+1 and the graph of x+y+z=e^(xyz) have a common point (0,0,1). Find the angle between the two corresponding tangent planes respect to these two graphs at point (0,0,1). In addition, find the tangent line of the curve intersected by these two graphs at point (0,0,1).

1. The scenario is the same as this (with a circular cross section): http://upload.wikimedia.org/wikipedia/commons/c/cf/Poutre_flexion_deviee.svg 2. Do I simply calculate the stresses from each bending moment and add them together? Or take the resultant vector and calculate...

So I've encountered many "what is the projection of the space curve C onto the xy-plane?" type of problems, but I recently came across a "what is the project of the space curve C onto this specific plane P?" type of question and wasn't sure how to proceed. The internet didn't yield me answers so...

Equation of plane containing points (a,0,0) (0,b,0) (0,0,c) Vectors <-a,b,0> <-a,0,c> Normal vector <bc,ac,ab> Plane Bc(x-a)+ac(y-b)+ab(z-c)= Bcx+acy+Abz=3abc Book is showing = abc

Let x \in \{-1, 1\}^n and let p(x) = \{w \in \mathbb{R}^n : x \cdot w > 1\}. What is the probability that p(x_1) \cap \ldots \cap p(x_{n+1}) = \emptyset given that x_i are chosen uniformly at random?

write the equation of the plane x - 2y - 2z = 27 in the form r.\hat{n} = d done write down the distance of the origin from the plane and show that the point which is the reflection of the origin is (6, -12, -12) done A second point P has coordinates (-3,2,1). Find the direction cosines of...

Homework Statement Calculate the volume of a body given by plane ##z=0## and ##z=1## and ##x^2+y^2+z^2=4##. Homework Equations ##detJ=r^2sin \theta## for spherical coordinates The Attempt at a Solution ##V=\iiint_{T}^{}dV=\int_{0}^{2\pi }d\varphi \int_{0}^{1}dz\int_{\theta...

I have a question about the equation of a line Are the forms <x0+at,y0+by,z0+tz> And t=(x-x0)/a=(y-y0)/b=(z-z0)/c only for straight lines?

Homework Statement 2) In the variant of Atwood’s machine shown below, a mass slides on an inclined surface 40θ above the horizontal with a coefficient of kinetic friction μk = 0.15. The masses M1 and M2 are 1 kg and 2 kg, respectively. Which way does the pulley rotate? If the lowest point of...

Homework Statement Find the vector equation for the line of intersection of the planes 4x+3y−3z=−5 and 4x+z=5 r = < _, _, 0> + t<3, _, _> Fill in the blanks for the vector equation. Homework Equations The Attempt at a Solution I used the method of elimination of linear...

find the angle between planes: 2x + y + 3z = 5 2x + 3y + z = 7 could someone double check this for me, I got 135.58 while the book got 44.4 thanks :s

Homework Statement identify the point on the line of intersection of the two planes that is nearest to the point (2,1,1) not on this line p1: x + 2y - z - 1 = 0 p2: x + y + z - 3 = 0 Homework Equations The Attempt at a Solution I think I can find the line of intersection by...