Perpendicular Definition and 503 Threads

Why mathematicians defined that the cross product of vector A and B will be a vector perpendicular to them.

Homework Statement Given, force of constant magnitude, which is always perpendicular to the velocity of the particle & the motion takes place in a plane. What happens to its kinetic energy? Explain. Homework Equations Work energy theorem The Attempt at a Solution According to work energy...

Hi, I've found a derivation of the formula for the relativistic momentum where they considered a car crashing into a wall in the system of the car and in an inertial system that moves parallel to the wall (and therefore perpendicularly to the movement of the car). They argue that since both...

Homework Statement A projectile is launched at height h with velocity v with 0 degrees angle with respect to the ground from the bottom of an inclined plane with an angle of theta.Determine the particle's velocity so that it strikes the inclined plane perpendiculary. Homework Equations...

weight is the force of a body on a surface or on a rope. So why isn't it always perpendiculair to the surface, for example in a slope. When a slope is so steep that it's vertical, there is no weight. But when the slope is a little diagonal you talk about a weight (which faces down(to the center...

Homework Statement There are two moving objects. The velocity of the first object, u, is constant. The second object maintains a constant velocity, v, perpendicular to u. The distance between the two objects is x. What is the second object's acceleration, a, in that moment? The Attempt at a...

Homework Statement Two light beams collide head on. Calculate their relative velocity. (c) A particle moves north at speed 0.85c relative to an observer standing on the Earth. What is the velocity of this particle as observed by a fast ship traveling east on the Earth at speed 0.9c? Give the...

How do I find the vector equation of the line which passes through (-3/2,-3/2,1/2) and is perpendicular to both x+1=y/3=-z and 2x+1=2y+1=z-5/2 I know how to do it using one equation but I am unsure about how to do it using two equations Thanks

I saw a link on MIT open courseware proving grad operator yields perpendicular vector to contour, but I can't make sense of how dg/dt=0. Can someone explain to me please...

I think its a defination to have infinite longitudnal lines , if line are not perpendicular than the infinite point will not add up to give the circumferance of equator, please help

Why is the force on a particle perpendicular to the magnetic field? In electric and gravitational field, the force is in the direction of the field. Is it due to the fact that electric and magnetic waves in electromagnetic waves oscillate at right angles to each other, or something else?

Consider the rotation of a rigid body about a fixed axis z, not passing through a principal axis of inertia of the body. The angular momentum \vec{L} has a parallel component to the z axis (called \vec{L_z}) and a component perpendicular to it (called \vec{L_n}). I have some doubts on...

Homework Statement I have an a-b coordinate system which is skewed with an angle = 60 deg. I also have a particle position defined by vector V1 (a1, b1, 0) which follows the coordinate system. The problem I have is that I need to get V2 (a2, b1, 0) which is perpendicular to V1. Homework...

I was wondering how to approach building a bridge which must lie across to points of differing points (one end is elevated 5 cm off the ground), meaning the bridge lies at an angle across a 35cm expanse. How would you calculate the forces exerted on each member if the bridge does not lie...

Hi All, I have a situation were I need to evaluate the heat transfer coefficient of a horizontal surface. The surface has tubes within although I first used "flow across a bank of tubes", this has been untrue due to the air flow coming from above the surface flowing vertically (and...

Homework Statement two 50N are applied to the corner B and D , determine the moment of couple formed by the two forces by resolving each force into the horizontal and vertical component and adding the two resulting couples . Use the result to determine the perpendicular distance between the...

Hello! I've encountered a problem of find all points (x,y) on $f(x)=\frac{x-\sqrt{\pi}}{x+1}$ where there are tangent lines perpendicular to $y=-(1+\sqrt{\pi}x+7\pi e^{e^{{\pi}^{110}}})$ So I first found derivative and ended up with $f'(x)=\frac{1(x+1)-(x-\sqrt{\pi})(1)}{x^2+2x+1}$ and then...

in 3D assume two skew lines L1: x=x°+at, y=y°+bt, z=z°+ct, L2: x=x°°+ds, y=y°°+es, z=z°°+fs. therefore L1, L2 parallel vectors are respectively: v1= <a, b, c>, v2= <d, e, f>. if v1.v2= ad+be+cf= 0 (vectors are perpendicular), are the line L1, L2 considered perpendicular also or beside the dot...

Homework Statement Line perpendicular to a plane Plane: z(x,y)= 0.882531*x-0.346494*y+0.383108 P1(0.5;0.1;Z) P2(0.4;0.15;Z) Homework EquationsThe Attempt at a Solution z(0.5,0.1) = 0.7897 z(0.4,0.15) = 0.68414 vector n=ai+bj+ck vector P2P1 = (0.5-0.4)i + (0.1-0.15)j +(0.7897-0.68414)k...

Homework Statement (I roughly translate the problem statement from German) Given the vectors a = (1,-2,3) and b = (1,1,1), divide the vector a in two components a1 (parallel to b) and a2 (perpendicular to b). Homework Equations In a previous question of the problem, I found that: a.b = 2 a x...

Homework Statement 2 points A and B, B moves rectilinear with uniform velocity u and velocity of A is always aimed at B with magnitude being constant=v, initially, v is perpendicular to u and separation was L, time taken for them to collide? and equation of motion of A? (in terms of x and y...

i'm dumb, sorry

Problem: The vectors A and B together define a plane surface. Determine a vector of magnitude 3 that is perpendicular to that surface. What I am thinking is Vector A is on the x-axis and B is on the y-axis. Therefore, the vector that I must determine, runs along the z-axis which is 90 degrees...

Homework Statement four point charges are placed at the corners of a square as shown in the figure having side 10 cm.If q is 1μC then what will be electric field intensity at the centre of the square? Homework Equations 3. The Attempt at a Solution [/B] Half of diagonal a/√2 0.1/√2...

Homework Statement From Kleppner and Kolenkow Chapter 1 (Just checking to see if I'm right) Given vector A=<3, 4, -4> a) Find a unit vector B that lies in the x-y plane and is perpendicular to A. b) Find a unit vector C that is perpendicular to both A and B. c)Show that A is perpendicular to...

Homework Statement I have 2 perpendicular oscilations and I have to find the trajectory equation. $$x=A\cos\omega t\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, (1)$$ $$y=B\cos(\omega t+\Delta\phi)$$Homework Equations $$\cos (x+y) =\cos x\cos y -\sin x\sin y$$ $$\cos^{2} x+\sin^{2} x =1$$...

I understand the right hand rule and the equition, but why is the direction of the torque perpendicular to the force on the counter clockwise side of the force and crossing the rotational point?

this is getting me really worried, why and why is velocity perpendicular to acceleration in uniform circular motion? please help me in conceptual way and practice too

The pointed line is equator as well as perpendicular bisector.Right?

Okay I'm having a little trouble understanding a section of this proof about the product of the gradients of perpendicular lines given in my textbook. I'm going to type the proof out but there will be a link at the bottom to an online version of the textbook so you can see the accompanying...

Homework Statement By considering A x (B x A) resolve vector B into a component parallel to a given vector A and a component perpendicular to a given vector A. Homework Equations a x (b x c) = b (a ⋅ c) - c (a ⋅ b) The Attempt at a Solution I've applied the triple product expansion and...

Homework Statement http://postimg.org/image/tlvhadljz/ I am trying to find the component of weight perpendicular to the bar. Homework EquationsThe Attempt at a Solution I tried as shown and I got mgcos(theta) but I am supposed to be getting mgsin(theta)

Consider a simple textbook problem in two dimensional kinematics - say, a projectile motion problem. I know that the x- and y- components of motion are independent of one another but I don't understand why. I know this is true due to everyday observation - empirical evidence of this being the...

Homework Statement Jack and Jill are maneuvering a 3570kg boat near a dock. Initially the boat's position is https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char68.png2,0,9https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char69.pngm and its speed is...

Homework Statement V1 and V2 are different vectors with lengths V1 and V2 respectively. Find |V1 X V2| if V1 and V2 are perpendicular. Homework Equations V1 X V2 = |V1|*|V2|sin(Θ) The Attempt at a Solution Since sin(90) = 1, V1 X V2 = |V1|*|V2|. When I input this answer it says its incorrect...

Trying to solve a drawing task. The following has to be achieved: - Produce a Square (vertices of ABCD) - Cut line BC into two equal parts, label the point in between as M. - Draw a line between point M and A. - Divide angle of BMA into two equal parts. Label the location where the bisector...

Find in rectangular coordinates a unit vector which is: A. in the direction of E at P(2,3,-4)if $\overline{E}=(x^2+y^2+z^2)\left(\frac{xa_{x}}{\sqrt{y^2+z^3}}+\frac{ya_{y}}{\sqrt{x^2+z^2}}+\frac{za_{z}}{\sqrt{x^2+y^2}}\right)$; B. Perpendicular to the plane passing through M(1,-5,5), N(-2,4,0)...

Given $\overline{A}=-4a_{x}+2a_{y}+3a_{z}$ and $\overline{B}=3a_{x}+4a_{y}-a_{x}$. 1.Find the vector component of A parallel to B 2.Find the vector component of A perpendicular to B my solution for 1. $\overline{A}\cdot\overline{b}=-1.372$...

Homework Statement Is the line through (-2, 4, 0) and (1, 1, 1) perpendicular to the line through (2, 3, 4) and (3, -1, -8)? Homework Equations R = R0 + tV (for each line) The Attempt at a Solution If the lines are parallel, then the V for the two equations will be proportional to each other...

Homework Statement A red Archimedean spiral is fixed to the ground. An external motor turns a grey support clockwise at w, the support can only turn around itself. On the support there is one orange disk that doesn't turn around itself at start. A stem is on the support. That stem: - turns...

Hello, I have data from a simulation of galaxies with various properties and I want to retrieve the peculiar velocity. If we want to relate with real galaxy surveys, what we can measure from real data is the radial peculiar velocity. My question is, since we have a simulation i imagine we can...

Homework Statement Two thin wires of length L_1, L_2 were placed perpendicular to each other in half of their lengths. Wires are carrying current I_1 and I_2. Find the torque on each of those wires. Homework Equations \tau = \mu \times B = r \times F The Attempt at a Solution To...

Can someone please look at the diagram below and tell me how u1 is obtained. If it is through the use of m3 please explain how the gradient m3 is obtained.

Hi all, When you have a surface defined by F(x, y, z) = 0 where x = f(t), y= g(t) and z= h(t) and a point on this surface P_0 = (x_0, y_0, z_0) , could someone explain to me why a line through P_0 with direction numbers [\frac{dx}{dt}, \frac{dy}{dt}, \frac{dz}{dt}] is perpendicular to a...

for the line y=4x-2 there is one perpendicular line of which will enclose a triangle on the lines and the values of the y-axis whose area is 8. What is the equation of this line? Well, I chose the x value to be the height of the triangle and that would make the base $$B=(4x-2)+2+\frac{1}{4}x$$...

Hello guys, I've had the following discussion at work: We are currently using a suture with a nylon thread on a tissue, when the thread of the suture is tightened in a force equal to if we've put a 500 gram weight on both ends of the suture line (meaning both end are tied together to the...

(SOLVED) How to build a 3D random vector perpendic. to another vector Hi everybody, do you have an efficient method for build up a vector with random components which is perpendicular to another (unitary) 3D vector ? Context: I have to randomly select polarization vector (P) for...

Homework Statement can anyone explain/prove why the gradient vector is perpendicular to level curves? Homework Equations The Attempt at a Solution

find the values of k and m so that the line x+1/k = y-2/m = z+3/1 is perpendicilar to the plane through the points U(1,3,8) , W(0,1,1) , and v(4,2,0).PLEASE HELP ME THANKS ALOT :)

Hi, Given several vectors, which may be or not be orthogonal to each other, how to construct a vector perpendicular to them? In a sense of inner production being zero. To be specific, I have n vectors v_{N} of length N, where n<N. So the maximum rank for these vectors is n, which leaves...