1. ### How do I find a plane that contains two given lines?

Homework Statement a. Find a point at where these lines intersect b. Find the equation of a plane that contains the two lines. Homework Equations r[/B] = <1,3,0> + t<3,-3,2> r = <4,0,2> + s<-3,3,0> The Attempt at a Solution I correctly found the point of intersection to be...
2. ### B How to state the laws of refraction and apply them to....

How do i apply the laws of refraction to plane and curved surfaces. I have absolutely no idea how to even start on this one, its got nothing to do with the course, i am going to study. i need to understand this to move on but i genuinely have absolutely no interest in optics. I really can not...
3. ### I In a rifle scope, why is the reticle at the focal point?

In order for a conventional telescopic riflescope to function, it must invert the image two times. As a result, the light-rays travelling through the tube must meet at two focal points. With my limited knowledge of optics, i assume that parallell light going in through the objective will meet...
4. ### Help building a Wind Tunnel

Hi everyone, I am new and I hope I'm putting this in the right section. I am currently a Sophomore in High school and I am building a wind tunnel. It's not for a class but rather its is like an independent study. I have been into planes pretty much all my life and I am hoping to get a pilots...
5. ### Inclined plane problem

Homework Statement Two bodies with mass m1 and m2 are tied together with an inexstensible and massless string rolled over a massless pulley put at the top of the incline with angle 30 . m2=5 kg which is on the incline is blocked and T=10 N . m2 is let loose and the system starts moving freely...
6. ### Complex Plane

Homework Statement Homework Equations The Attempt at a Solution I'm not sure how to even begin this problem. My notes mentioned something about a Mobius Transformation but that's not something that I've been taught, and certainly not something I'm familiar with. Any advice would be...
7. ### MATLAB How to create distinct circles in Matlab?

I want to create a plate of distinct circles on Matlab where their radii are generated by randn(1,p) and centers are random. I am currently doing the circles using viscircles, but some of them are overlapping, and since I want approximately 100 ones, this problem only gets worse. How can I make...
8. ### Optics - spherical and plane mirror

Homework Statement A convex spherical mirror with a focal length of magnitude 24.0 cm is placed 22.0 cm to the left of a plane mirror. An object 0.300 cm tall is placed midway between the surface of the plane mirror and the vertex of the spherical mirror. The spherical mirror forms multiple...
9. ### Railgun-Powered Ramjet Design

Recently, I designed (in my head) a Hypervelocity Passenger Vehicle (just a cool name for really high speed transports). I immediately ran into engine design problems ( I like designing everything stand-alone), since regular jet engines can't get to Mach 8.8 without burning up into flames, and...
10. ### Find the equation of a plane perpendicular to a line and goes through a point

Homework Statement find equation of plane P that is perpendicular to line L which passes through the point (-2,-2,3) Homework Equations ... The Attempt at a Solution [/B]line L passes through the points (1,2,1) and (0,0,-3) I have worked out the parametric equations of line L to be x=1-t...
11. ### Finding the Magnetic Field Due to a Wire stretching from Infinity to 0

Homework Statement An intensity current I descends down the z-axis from z = \infty to z = 0, where it spreads out in an isotropic way on the plane z = 0. Compute the magnetic field. Homework Equations The only relevant equation I can think of is Ampere's Law, \oint_\gamma \vec{B} \cdot...
12. ### Let A, B, and C be vectors in R3...prove r lies in a plane

Homework Statement ##\vec { \dot { r } } =(t+1)\vec { A } +(1-sint)\vec { B } \quad \vec { r(0) } =\vec { C } ## a. Find an equation of the tangent line to the curve at ##\vec { r(0) } =\vec { C } ##. b. Use a definite integral to find ##\vec { r(t) } ## c. If ##A## and ##B## are non...
13. ### Given the planar curve, find the equation of the plane

Homework Statement r(t) = < 2e^t - 5 , e^t +3t^2 , 4t^2 +1> Is a curve that lies within a plane. Find the equation of this plane. The Attempt at a Solution I am not sure if my approach is correct. These are my results: x=2e^t - 5 y = e^t +3t^2 z = 4t^2 + 1 z = 4t^2 + 1...
14. ### Colinear points in a vectorplane

Homework Statement If a, b and c are coplanar vectors related by λa+μb+νc=0, where the constants are non-zero, show that the condition for the points with position vectors αa, βb and γc to be collinear is: λ/α + μ/β + ν/γ = 0 Homework Equations Dot product Cross product Tripple product Vector...
15. ### Find magnitude of two velocities, with one at an angle?

Here is the problem: I am sure I can use pythagorean theorem of quadratic equation to solve but to be honest I'm blanking ridiculously. I have tried setting it on a coordinate grid and finding the resultant, but I have had no luck! I know I've done this problem before in highschool but I'm...
16. ### Induced EMF in bent loop

Homework Statement The figure below shows a closed loop of wire that consists of a pair of equal semicircles, of radius 7.0 cm, lying in mutually perpendicular planes. The loop was formed by folding a flat circular loop along a diameter until the two halves became perpendicular to each other...
17. ### Proof involving central acceleration and vector products

Homework Statement Suppose r:R\rightarrow { V }_{ 3 } is a twice-differentiable curve with central acceleration, that is, \ddot { r } is parallel with r. a. Prove N=r\times \dot { r } is constant b. Assuming N\neq 0, prove that r lies in the plane through the origin with normal N. Homework...
18. ### Find the equation of the plane parallel to two lines

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 Equations The...
19. ### Distance from a point to a plane

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...
20. ### A plane through three points

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...
21. ### Reflection in a Plane Mirror

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...
22. ### B Proof in RxRxR

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...
23. ### Rubber band propelled plane

Hello PF! I have a project/competition in freshman college Aerospace that calls for a plane that can stay in the air for as long a time as possible while going as far as possible. The requirements don't explicitly say we need rubber bands as a propulsion but pretty much prohibit everything but...
24. ### Does the line lie in the plane?

Homework Statement Does the line through the point P(1, 2, 3) with direction vector d = (1, 2, -3) lie in the plane 2x+y-z=3? Homework Equations The Attempt at a Solution From the 2x+y-z i can get the vector (2, 1, -3) and the direction vector, their dot product does not equal zero. So, no...
25. ### Snow sled on a hill

Homework Statement Say you push a sled of mass m up a hill that is angled upwards at a certain angle \theta at a constant velocity. The hill has snow on it offering a friction force that is equal to 30% of the sleds weight. If you pushed the sled down the hill with the same amount of force...
26. ### Calculating acceleration of plane when given mass, friction force and Vi

Homework Statement A 2000 kg plane is landing at an airfield with an initial speed of 50 m/s. The force of friction is 1/4 the weight of the plane. What is the acceleration of the plane? Homework Equations Fnet = ma Fnet = something - ff The Attempt at a Solution 2000a = thing I don't know...
27. ### Can spin be modeled as a spinning vector until "measured" ?

I was wondering it the projection of the measurement axes onto a spinning vector modelled by a plane would produce correlations of entangled particles in line with what is found by experiment. Does anyone know of any discussions on this subject? Would this lead to stronger correlations than spin...
28. ### Paper Plane Distance

Hi, I'm doing an experiment to get my silver CREST award, in which I've created a mechanical paper plane thrower. I have thrown various types of plane, but all with the same design. The thrower uses a 9V battery, but is more like 6 now. The thrower has two motors, each which take 70mA. The...
29. ### Weyls representation of a propagating (z-v*t) spherical wave

Hello! The following wave solves the 3D wave equation: $$\frac{\sin\left(k\sqrt{x^2+y^2+\frac{(z-vt)^2}{1-\frac{v^2}{c^2}}}\right)}{\sqrt{x^2+y^2+\frac{(z-vt)^2}{1-\frac{v^2}{c^2}}}}\cos\left(w\frac{t-\frac{vz}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}}\right)$$ This is a propagating standing spherical...
30. ### At what angle should the bomb be released?

Homework Statement There is a plane flying at 200 km/h and wants to drop a bomb on a car traveling 130 km/h which is 78.0m below the plane. at what angle should the bomb be released? the answer is 45 degrees. Homework Equations sine law: SinA/a= SinB/b cosine law: a^2=b^2+c^2+bcCosA v=d/t...