What is Perpendicular: Definition and 506 Discussions
In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects.
A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles. Perpendicularity can be shown to be symmetric, meaning if a first line is perpendicular to a second line, then the second line is also perpendicular to the first. For this reason, we may speak of two lines as being perpendicular (to each other) without specifying an order.
Perpendicularity easily extends to segments and rays. For example, a line segment
A
B
¯
{\displaystyle {\overline {AB}}}
is perpendicular to a line segment
C
D
¯
{\displaystyle {\overline {CD}}}
if, when each is extended in both directions to form an infinite line, these two resulting lines are perpendicular in the sense above. In symbols,
A
B
¯
⊥
C
D
¯
{\displaystyle {\overline {AB}}\perp {\overline {CD}}}
means line segment AB is perpendicular to line segment CD. For information regarding the perpendicular symbol see Up tack.
A line is said to be perpendicular to a plane if it is perpendicular to every line in the plane that it intersects. This definition depends on the definition of perpendicularity between lines.
Two planes in space are said to be perpendicular if the dihedral angle at which they meet is a right angle (90 degrees).
Perpendicularity is one particular instance of the more general mathematical concept of orthogonality; perpendicularity is the orthogonality of classical geometric objects. Thus, in advanced mathematics, the word "perpendicular" is sometimes used to describe much more complicated geometric orthogonality conditions, such as that between a surface and its normal.
Hydrostatic Pressure Force "must" be perpendicular
Hi, I'm taking AP Physics B and we started learning about fluids and pressure. My teacher told me that the pressure of a fluid acting in a a container only applies a perpendicular force to the sides, which doesn't make sense. If you 'zoomed...
Finding parametric equations for the line through the point that is perpendicular to plane and parallel?
What is the difference when finding parametric equations for a line through a point that is perpendicular vs. parallel? Surely there must be some difference but I cannot seem to figure it...
Homework Statement
The vector a = [2,-5,6] is given. Determine one vector that is perpendicular to a.
Homework Equations
Cross product or dot product
The Attempt at a Solution
I messed around with the dot product by making the right side 0 because cos 0 = 90 but i don't think i...
Homework Statement
What will be the net magnetic field at a point, if two mutually perpendicular magnetic forces are acting on it?
Homework Equations
The Attempt at a Solution
A pair of perpendicular vectors...
√Homework Statement
This thread contains 2 questions that are similar.
A pair of 482.5 N vectors are perpendicular.
What is the magnitude of their resultant?
Answer in units of N
Two vectors of magnitudes 24 N and 31.1 N
act at right angles to each other...
Okay, I feel like I am just missing something that should be very easy to see, but I can't seem to wrap my head around this concept. Can anyone explain to me why a force perpendicular to the momentum only changes the direction of the momentum and not the magnitude?
By my logic, if...
Okay, I feel like I am just missing something that should be very easy to see, but I can't seem to wrap my head around this concept. Can anyone explain to me why a force perpendicular to the momentum only changes the direction of the momentum and not the magnitude? By my logic, if Fnet=Δp/Δt...
Homework Statement
Consider a plane with the outer normal unit vector of (1/√2, -1√2, 0). There is a force of (2,1,5) acting on the surface. What is the component of force normal and parallel to the plane? What is the maximum parallel component to the plane?
I would like to check my answers...
Determine the resultant moment at support points A and B due to the forces acting on the truss as shown.
Fx = F(cos∅), Fy = F(sin∅), M = F(distance)
Point A -88.98kN*m
Point B ?
I have no problem calculating most of the forces, but I'm lost when it comes to knowing what to...
Homework Statement
Determine the components of F that act along rod AC and perpendicular to it. Point B is locateda distance f along the rod from end C http://imgur.com/iGJkN
Given:
F = 600 N
a = 4 m
b = 6 m
c = 4 m
d = 3 m
e = 4 m
f = 3 m
I have no clue where to start. please help!
Homework...
Homework Statement
this website has the question listed as #2-116. the solution shown is extremely complicated and i ask thet someone please help.
http://www.scribd.com/doc/48470460/113/Problem-2-116
Homework Equations
The Attempt at a Solution
I apologise in advance for an extremely trivial question, i am returning to brush up on some basic maths and can't seem to arrive at the answer
Find the coordinates of the foot of the perpendicular from the point A with coordinates (-5,5) to the line 10x+2y-3= 0
1.) gradient of original...
Why do magnetic fields only apply force to charges/currents that are perpendicular to the field?
Does it have something to do with the orientation of the field created by the moving charge in relation to the field it is in?
Hi
I am making a solar system emulation. I need some fairly precise velocities for the planets as a start velocity of the planets and since i calculate the gravity i need it perpendicular in a known distance from the sun.
First of all.. is it correct that if i calculate gravity i would...
Homework Statement
The question is as attached in the picture.The Attempt at a Solution
I understand and got the answer to part (a) but from (b) onwards I am completely lost. Here are my assumptions:
1)Edges of 'cube' are still of length a
2)Successive planes are parallelBut, there is some...
Homework Statement
Suppose v = <-3,-2, 1> and w = <-1,1,1>. Then
projw(v) = < -2/3, 2/3, 2/3 > ,
and the component of v perpendicular to w is?
Homework Equations
The Attempt at a Solution
I understood how to get the projection, and tried using the component formula...
http://img580.imageshack.us/img580/8859/proofea.jpg
i am having trouble figuring out how to proceed without knowing anything about the function ψ=ψ(x,y,z). all i know is that it's a function of x,y,z. but how can i figure out how the surface changes w.r.t the tangent vector if i don't even...
Homework Statement
Find a unit vector in the xy plane which is perpendicular to A = (3,5,1).
Homework Equations
A_x{B_{x}} + A_y{B_{y}} + A_z{B_{z}} = \textbf{A} \cdot \textbf{B}\\\hat{\textbf{A}} = \frac{\textbf{A}}{|\textbf{A}|}
The Attempt at a Solution
In order to be perpendicular...
A math question about projections of lines: Say we have two straight lines which we consider as number lines (\mathbb{R}). I've learned that a projection of one line onto another is of the form ax + b for a,b\in \mathbb{R} when the two lines are parallel. If we allow the possibility that the...
For an arbitrary distance the equation is:
\sqrt{\Sigma_{i}^{n}x_{i}^{2}}
I would like to know what are the proofs for higher dimensions being perpendicular to our 3-spaital dimensions. If I am wrong in any way, please elaborate.
I guess what I'm saying is since:
r^{2}=x^{2}+y^{2}...
Homework Statement
velocity changes when force applied perpendicular
i can't understand a simple question.
can u help me
what i know is that speed in short its magnitude does not change when force is applied perpendicular.its direction only changes so does the velocity.
what i don't...
What does the the cross product of two acceleration vectors do?
(a cross ar) = 0
where a =axi + ayj + azk and ar = arxi + aryj + arzk
(a cross ar)x = ay*arz - az*ary
(a cross ar)y = az*arx - ax*arz
(a cross ar)z = ax*ary - ay*arx
It gives the perpendicular components of each.
In the...
Homework Statement
Let \vec{a},\vec{b},\vec{c} be three constant vectors drawn from the origin to the points A,B,C. What is the distance from the origin to the plane defined by the points A,B,C? What is the area of the triangle ABC?
Homework Equations
The Attempt at a Solution
Starting...
Homework Statement
An infinite metal plate occupies the xz-plane. The plate is kept at zero potential. Electrons are liberated from the plate at y = 0. The initial velocity of the electrons is negligible. A uniform magnetic field B is maintained parallel to the plate in the positive z-direction...
An electromagnetic wave is a variation in the electromagnetic field. How wide is the variation in the field caused by a wave? I mean, what is one wave's distribution perpendicular to the direction of the wave's progression? This distribution obviously increases in magnitude if two or more waves...
I've got a problem with perpendicular planes in Matlab.
I start with a plane A and a point P in A. I calculate a plane B perpendicular to A through point P. Equation plane A: -21660x + 1036y + 4669z = 9.22e6
Point P: [129, 46, -1925]
If [a,b,c] is the normal vector of plane B, I choose b = 0.5...
the way to find out if a vector is perpendicular to a plane
the usual way is to find the normal to the plane, then find the cross product of the normal with the vector you are given. if it is 0 then perpendicular, else it is not correct?
what i want to know is, can you also, put the the...
Homework Statement
Given a W21x68 beam with 1.388 kips per foot loading spanning 34 feet. The beam will carry the load but the maximum deflection is greater than wanted. We would like to put a W33x118 beam perpendicular to the centerline of the W21x68 (17 feet), to limit the deflection...
Homework Statement
There are two known vectors (you can make up any two, the question gives them but I don't know what they were) and I need to find a vector that is perpendicular to both of them.
Homework Equations
Dot Product
The Attempt at a Solution
Getting two equations with three...
Homework Statement
Find a vector equation of the line l containing the points (1,3,1) and (1,-3,-1). Find the perpendicular distance of the point with coordinates (2,-1,1) from l.
2. The attempt at a solution
Let (1,3,1) = a, let (2,-1,1) = q. Let N be the point where ANQ = 90 degrees...
I have read about how magnetism arises from electric interactions and relativity. But in that respect i don't see how perpendicular wires can exert magnetic forces on each other. The movement of the charges is perpendicular so length contraction does not occurr in the direction of the current...
Homework Statement
Consider the line perpendicular to the surface z=x^2+y^2 at the point where x = −1 and y = 2 Find a vector parametric equation for this line in terms of the parameter t.
The Attempt at a Solution
I wasn't quite sure how to go about with this problem so I just went along with...
Hi all,
How do you find out if this Parametric equation
x = -2t + 3 ; y = -t - 1 ; z = -3t + 2
Is perpendicular to this parametric equation
x = -2 + 6t ; y = 3 - 6t ; z = -3 - 2t
Thanks
Stephen
Homework Statement
The idea is that we have a current in a wire, and the B magnetic field is to be known in a specific point P. This point P is in the same straight line as the part of the wire we are interested in.
For example, in the attached image the problem would be to know the field...
I am working on a software for analysis of brain connections using MRI.
Please suggest the simplest way to find a vector which is:
perpendicular to a unit vector that is positioned in the coordinate center,
it should be in the 2D plane containing the given vector and a given point on...
Topic. If I have an iron shaped like a bar magnet placed flat on the floor, can the poles of the magnet be pointing anywhere else other than 90 degrees and 180 degrees?
Just a quick question here. Have I done this correctly? Do I need to factor in the 3 from L?
Many thanks.
Homework Statement
Q. Verify that the lines L: x -2y + 3 = 0 & K: 2x + y = 0 are perpendicular.
Homework Equations
The Attempt at a Solution
x(x) + y(y) = 0 => 1(2) +...
http://en.wikipedia.org/wiki/Drag_coefficient
from wikipedia, it is written 1.98-2.05 for flat plate perpendicular to flow(2D) , but I have a differrent b/h ratio plate, where h=157mm and b=816mm , b/h=5.197
how to get the drag coefficient in this case?
Thanks.
Hi there,
The two given lines:
1) x / 2 = (y-1) / 2 = z
2) x + 1 = y – 2 = (z + 4) / 2
I need to find the common perpendicular between them.
Though when I tried to calculate the distance between them, I get 0.
Can someone please help?
Thanks in advance
Hi there,
The two given lines:
1) x / 2 = (y-1) / 2 = z
2) x + 1 = y – 2 = (z + 4) / 2
I need to find the common perpendicular between them.
Though when I tried to calculate the distance between them, I get 0.
Can someone please help?
Thanks in advance
Homework Statement
Prove the following or disprove with a counterexample: Let f be a differentiable function in an open set U in R^3 and (a, b, c) be a point in U where the gradient of the function f isn't zero. If r: I -> U is a regular curve with a regular derivative on an open interval I...
Position and acceleration vector -- parallel and perpendicular
Homework Statement
The motion of a particle is defined by the position vector
r = A(Cos t + t Sin t) i + A(Sin t + t Cos t) j where t is expressed in seconds. Determine the values of t for which the position vector and...
Why is it that the normal force always point perpendicular to the plane? If I imagine the ground as made up of a bunch of particles I find it hard to see, why they should necessarily direct their forces perpendicular to the plane. Consider as a classical example a box sliding down a slope. The...
Find a nonzero 3x3 matrix A such that Ax is perpendicular to [1,2,3] for all x in R3
A vector perpendicular to [1, 2, 3] could be, say, [-2, 1, 0]. But what would be a general approach to finding a solution that would satisfy all x? Thanks!
Prove that, if (c - b).a = 0 and (c - a).b = 0, then (b - a).c = 0. Show that this can be used to prove the following geometric results:
a. The lines through the vertices of a triangle ABC perpendicular to the opposite sides meet in a point.
b. If the tetrahedron OABC has two pairs of...
Prove that, if (c - b).a = 0 and (c - a).b = 0, then (b - a).c = 0. Show that this can be used to prove the following geometric results:
a. The lines through the vertices of a triangle ABC perpendicular to the opposite sides meet in a point.
b. If the tetrahedron OABC has two pairs of...