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.
I have some understanding, but I'm not sure about how accurate it is:
Electrostatic force is given by F = qE, where F and E are both vector quantities. If the dot product of either side and the displacement vector Δs along an equipotential line is taken, the equation becomes
F⋅Δs = qE⋅Δs.
F...
The question that I'm trying to answer states "Make a vector equation of a plane that is perpendicular to the z axis." How do i ensure its perpendicular? How do i start this equation?
Another question similar to this that i am also struggling states "What is the vector equation of a 2D line...
Homework Statement
[/B]
Consider the line whose shortest distance to the origin is 5 and that is perpendicular to the ray ##\theta= \frac {5*\pi}{7}## for r>0
Find its polar equation ##r=r(\theta)## and ##\theta_1<\theta_2## in the interval ##[0, 2\pi]## such that ##r(\theta)\geq 0## for all...
Homework Statement
Describe how the dot product can be used to determine whether two vectors are perpendicular. Create a question with vectors in 3-space to illustrate this property. Solve the question as well.
Homework EquationsThe Attempt at a Solution
Did I do this right? I did something...
My question is perhaps as much about the philosophy of math as it is about the specific tools of math: is perpendicularity and rotation integral and fundamental to the concept of multiplication - in all number spaces?
As I understand it, the product of complex numbers x = (a, ib) and y = (c...
Homework Statement
Two particles A and B each carry a charge Q and are separated by a fixed distance D. A particle c with charge q and mass m is kept at the midpoint of A and B. If C is displaced perpendicular to AB by a distance x where x<<<D,
find the time period of the oscillation of the...
$\textsf{Find the vector perpendicular to the plane PQR
determined by the points}$
\begin{align*}\displaystyle
&P(2,1,3), \, Q(1,1,2), \, R(2,2,1)\\ \end{align*}
$$\textbf{ solution:}$$
\begin{align*}\displaystyle
\vec{PQ}&=(1-2)i+(1-1)J+(2-3)k=&-i-k\\...
An assumption in deducing the Bethe equation is that the momentum transfer is perpendicular to the direction of the particle.
ALSO
In Allison & Cobb (1980), just after eq. 28, they state that the first two terms of the Photoabsorption Ionization model arise from the magnetic vector potential...
The question:
The line L1 has equation r = \left( \begin{array}{ccc}4 \\-1 \\0\\\end{array} \right) + t\left( \begin{array}{ccc}1 \\1 \\-1\\\end{array} \right) , and point A has coordinates (4, 8, -3).
Find the coordinates of point B on L1, such that \overrightarrow{AB} is perpendicular to...
Does anyone know where I can find information about how to calculate how much extra energy is required of a spaceship to try to thrust perpendicular (or at some angle) to the orbital plane verses flying completely/only in the orbital plane when moving outwards in our solar system? If the...
i would like to know if the forces exerted by the load on pulley 1 and 2 are equal when the motor star running , or if in pulley 1 is exerted more force because the location of the load at the end of the lifting platform. The lifting platform only moves vertically, restricted by rails. What I...
I am asking this because ∇ is also considered as a vector in some cases. Considering it as a vector in this case ,too,
( ∇× E).E = (- ∂ B/∂t).E = - ∂ (B.E)/∂t =0
Since B and E could be arbitrarily dependent on t,
B.E = 0
where B and E are magnetic and electric fields respectively.
This...
Not only the Problem I have attached in Picture, but there are few more where I get different answer while solving by taking Moment Component and by Common Perpendicular.
[NB : The problem Stated in 'Engineering Mechanics' by Ferdinand L. Singer. Process 3 is what I did, Process 1 is what is...
The tangent passes through just one point
Now i can draw it such that the angle of incidence is always 0 and incident angle is always 90
Then no image will be formed.
Why does this not happen??
If the normal is always 90 to the mirror can we assume that it always passes through centre of curvature?
The light rays passing through the centre are reflected back in the same direction as angle of incidence is 0
and incident angle is 90
so, the normal should pass through the centre.
Homework Statement
Car 1: 2200kg
Initial direction: South
Car 2: 1800kg
Initial direction: East
Cars lock together and slide 11.25M (S 22.25 E)
At an acceleration that is 9.81 m (back) (it's a coincidence that this is gravity.)
Homework Equations
Who's fault was the collision if the speed limit...
Two smooth spheres of masses km and m collide obliquely. the sphere of mass m is brought to rest by the impact. the coefficient of restitution for the collision is 1/k (k greater or equal to 1) Prove before the impact the spheres were moving perpendicular to each other.
i have worked out k=-1...
two smooth spheres of masses 2kg and 4kg collide obliquely . the 2 kg mass is brought to rest. the coefficient of restitution is 1/2
prove before the impact the spheres were moving in perpendicular directions to each other.
using conservation of momentum. 4x+2y=4p+2(0) where x...
Homework Statement
Find the unit vector perpendicular to the level curve of f(x,y) = x2y-10xy-9y2 at (2,-1)
Homework Equations
Gradient
The Attempt at a Solution
I'm not sure what it's asking. Wouldn't this just be the gradient of f(x,y) evaluated at (2,-1) then normalized? or am I missing...
Homework Statement
A particle of mass m1 collides with a particle of mass m2 initially moving at right angles to it(see Figure 1 below). Calculate the final velocities of each particle, and the angles at which the particles leave the collision site( as measured with respect to the original...
Homework Statement
So the problem is the following : we observe the stellar aberration of a star which isn't on the zenith, so that the star forms an angle theta with the ecliptic plane of the Earth. With such a position, the star will describe an ellipse instead of a circle (typical movement...
Hi there. I very much enjoy this forum and have been doing so for a while.
I have a problem and I am not sure of the explanation I came with.
Suppose there is a plane that is nosediving perpendicular to Earth. What will the "passengers" feel? In the first seconds the acceleration will be equal...
Homework EquationsThe Attempt at a Solution
[/B]
I was of the understanding that the slope can be calculated as mgsin20 whereas the force acting straight down through the lift is mgcos20 but the answer is mg divided by cos 20??
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...
Hello to everyone, merry christmas and happy new year! I was trying some exercises on the Feynman Lectures, on the topic of statics, and I came across with a problem which, simplified until where I am stuck, asks for the tension of a cable perpendicular to a bar with a weight on the top of it...
Picture water flowing in a duct. In these kinds of scenarios, the loading exerted by the moving fluid to the solid in the perpendicular direction is often taken as being equal to the pressure of the fluid at the wall.
I agree that the above assumption is true for a stationary fluid. For a...
Homework Statement :[/B]
A mass is moving with constant acceleration in the x-y plane. At time t = 0s the mass’s position is 2mˆı+3mjˆ, the mass’s velocity is 3 m/s ˆı −4 m / s jˆ and the mass is subject to an acceleration of 1 m/ s ^2 ˆı + 1 m/ s^ 2 i jˆ.
At what time is the velocity...
Homework Statement
A particle flies along in the positive +x direction. It has a constant force F applied 30º clockwise to the x-axis.
It is moving at .6 c. What is the angle of acceleration?
Homework Equations
a = F/(mγ3)
The Attempt at a Solution
[/B]
I'm pretty sure I know how to do...
Say i Have
1. A perfectly spherical and perfectly rigid Ball
2. A perfectly flat and perfectly rigid wall
Say i throw the ball at my FLAT wall also giving the ball a linear velocity
The only contact with the wall and the ball is a point... a POINT !
So, I can as well forget about the rest of...
I mean physicists when they have to create a field they draw it with the same direction of the force, (gravitational, electric for example) i know that the magnetic field acts only on moving charges and i also know that the force is a relativistic effect of lorentz contraction, but why creating...
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...
Homework Statement
##W = x^2+5y^2##
Show that ##\nabla W## is perpendicular to the level curves of W at ##(X_0, 0)##
Homework Equations
##\nabla f(x,y) = <\frac {\partial f} {\partial x} , \frac {\partial f} {\partial y}>##
The Attempt at a Solution
I know that the gradient is always...
The no slip condition has been described as the adhesion of a fluid to a solid surface setting the relative fluid velocity to zero - cohesion (viscous stress) between fluid elements spreads evenly the velocity gradient through the boundary to the free stream.
This also infers that the pressure...
Homework Statement
Proof that if the slopes of two lines a1, a2 (that are not vertical), m1,m2 satisfy:
m1*m2 = -1, then the lines are perpendicular.
Homework EquationsThe Attempt at a Solution
I tried to use the tan function, so that m1 = tanΘ where Θ1 is the angle of the line formed from x...
Homework Statement
Imagine two motorcycle gang leaders racing at relativistic speeds along perpendicular paths from the local pool hall, as shown in Figure 1.21. How fast does pack leader Beta recede over Alpha’s right shoulder as seen by Alpha?
Solution Figure 1.21 shows the situation as seen...
I am given the following problem: Show, using vectors, that the diagonals of an equilateral parallelogram are perpendicular.
First, imagine that the sides of the equilateral parallelogram are the two vectors ##\vec{A}## and ##\vec{B}##. Since the figure is equilateral, their magnitudes must be...
Homework Statement
The book ("Real World Physics") says
A virtual image in a plane mirror is on the perpendicular from the object to the mirror
Homework Equations
I know that the normal line is perpendicular to the surface of the mirror
And I know that the angle of the incidence and reflection...
Hello!
I'm currently studying Projectile Motion and Motion in Two Dimensions now in Physics class, and I happened to quickly jot down what my teacher said onto my computer. I came across the note and it says "Vector forces cannot be perpendicular to each other." I'm a little unsure of what is...
I am struggling with this question, it would be easy enough if the triangle was equilateral but that is not necessarily the case.
Let (ha, hb, hc) be heights in the triangle ABC, and let Z be a point inside the triangle.
Further to this, consider the points P, Q, R on the sides AB, BC and AC...
I am looking for a family of curves where if we consider one curve of them and get the tangent of that curve at any arbitrary point on the curve, then you will always find a point in the other curves where the tangent of this point is perpendicular to the tangent of the first point.
My guess...
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...