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.
Homework Statement
My question is to :
Prove that the perpendicular bisector of the two points (x1, y1) and (x2, y2), in general form, is given by
Ax + By = C
where
A= 2(x2-x1), B= 2(y2 -y1) and C= y2^2 - y1^2 + x2^2 - x1^2
Help me with this proving things.
Thanks...
Homework Statement
how do I find the basis for all vectors that are perpendicular to both
v1 = (1,1,0,0) and
v2 = (1,0,1,1)
If it were 3-D I could find a normal vector via cross product, but in n-dimensions... what do I do?
My one thought is to arrange and solve linear homogeneous system...
Homework Statement
Two perpendicular forces, one of 45.0 N directed upward and the second of 60.0 N directed to the right, act simultaneously on an object with a mass of 35.0 kg. What is the magnitude of the resultant acceleration of the object?
A. 8.68 m/s^2
B. 3.00 m/s^2
C. 5.25 m/s^2
D...
Homework Statement
Find the values of k such that lines 3kx+8y = 5 and 6y -4kx = -1 are perpendicular.
I don't need the answer, but a push in a right direction. However, feel free to solve the equation :)
Homework Equations
1. Slope of a line is m = [y2-y1]/[x2-x1] where we have 2...
Please help me! I have been sitting with this problem for god knows how long, and I just can't figure it out. I've tried re-reading the problem text, re-reading the chapter, reading alternative explanations on the web, drawing the problem on paper -- heck, I've even tried shouting at it -- but...
ok so I'm working on a few problems on my physics homework and I got stuck:
On the first one I answered the first question, but I don't know how to approach the 2nd and 3rd parts... what formulas would i use? and on the 2nd questions, I thought i needed more information than just the time, I...
This is an interesting question that my friend had...
Is the zero vector perpendicular to all other vectors?
We know that the zero vector is orthogonal to all other vectors; I verified this in both "Linear Algebra and it's Applications" by Strang and "Calculus" by Stewart; both are...
Hey, just hoping sum1 new a better way to do the follwing Q other then the way I'm doing it!
it gives 2 vector eqn's of lines L1 and L2 as follows:
L1 = r = (2i+4j)+k(-1i+3j)
L2= r = (-3i+1j)+m(6i+2j)
(ie k= lambda and m=mew- also they are inform matrice form but i didnlt now how to...
Suppose an object is moving at some veocity v. Why is it that if you apply a force in the direction perpendicular to the direction of velocity, you only change the direction of the velocity and not its magnitude.
I am having a feeling that I am going to get one of those "that's just the way...
I am having a lot of trouble trying to figure out ot do this problem. The problem states that Two objects, A and B are connected by a rigid rod that has a length of 60m. The objects slide along perpendicular guide rails. If A slides to the left witha constant speed of 62m/s along the x-axis...
i am given parametric equations of 2 lines L1 and L2 and i am asked to find the vector, parametric and symmetric equation of a line that intersects these 2 lines at 90 degrees so a line that is perpendicular to those 2 lines. how do i go about this? at first i tried converting the parametric...
Sir/Madam,
1)The 2 adjacent walls and the ceiling of a rectangular room are mirror surfaced.What is the number of images of himself does an observer sees?
If it was the case of 2 mirrors I know it is 3. But here there are 3 mirrors which are mutually perpendicular. But if we take 2 mirrors at...
how do i find the b field of two perpendicular wires.
suppose one wire is pointing out of the page and the other one is going from left to right. I am looking for the magnetic field between them.
o (wire going out of paper)
B=?
xxxxxxxx (wire going left to right)
Hey. Here is the question:
\underline{b}= -8\underline{i} - 6\underline{j}
I need to find a unit vector perpendicular to vector b.
Ive come up with the following:
10 \times |\underline{x}| \cos 90 = \underline{b} \bullet \underline{x}
I don't know if what I've done is even...
A box with a mass of 22kg is at rest on a ramp inclined at 45 degrees to the horizontal. The coefficient of friction between the box and the ramp are us = 0.78 and uk = 0.65.
a) Determine the magnitude of the largest force that can be applied upward, parallel to the ramp, if the box is to...
Does perpendicular incident light slow down through glass? When light travels through glass at a perpendicular angle, there is no refraction and hence no bending. If it slows down through glass, does that mean that red will emerge first and violet last?
The question reads:
"Consider the surface given by the equation x^3 + xy^3 - z^2 = -4 The point p = (1,2,3) lies on this surface. Give a vector that is perpendicular to the surface at p?"
I'm not too confident about this question although there is a theorem in my notes saying:
if p...
Hi, can someone help me out?
In the question there are two straight rods which are connected at their ends in such a way that they are perpendicular. (As a visual aid, the situation can be seen by picturing the usual right handed xyz system of coordinates, with each of the two connected rods...
Hi. I'm having some trouble trying to grasp a concept. I know that mathmatically Force perpendicular to motion is zero work. I can't seem to grasp this conceptually. First It seems That is an object is moving right and a force acts straight up on it, it will cause the object to move in a...
How can i proove if this line is perpendicular to this one?
Line
x=-2-4y, y=3-2t, z=1+2t
Plane
2x+y-z=5
I don't care that much about the answer, I want the procedure.
I've been having trouble with lots of basic geometry, including a lot of things regarding planes and intersection of planes.
My question is, how would I get the equation of a plane (given a point on the plane), which is perpendicular to the line of intersection of two other planes?
I am...
I don't know if I'm having a brain fart or what but I'm drawing a blank...:smile:
What is the slope of a line perpendicular to x - 3y = 9?
Notes:
Perpendicular lines have slopes that are negative reciprocals of each other.
Example: So, if the original line has a slope of -3/2, the...
Determine whether the point W(2,-1) lies on the perpendicular bisector of line segment UV, endpoints U(3,5) and V(-3,-1). Explain and justify your answer.
I can't figure it out, if someone could, it would be a pleasure! (it is a grade 10 question)
I have a curve -\sqrt {2x^3 } on which I'm supposed to draw a tangent that is perpendicular to the line \[y = \frac{4}{3}x + \frac{1}{3}.
I know that this tangent must have a "steepness" of -3/4 in order to make it perpendicular, but how do I now find the point on the graph?
How would you go about finding a perpendicular vector, to two 3 dimensional vectors? One way, I solved is using the cross product of the two vectors. Splitting the i's j's and k's up and solving using a determinent. But, what's another way to do it?
solving perpendicular oscillation problems-- lissajous
Hi all.
Ok, I am not getting how we're to solve perpendicular oscillatory systems.
How do the variances in frequency, and phase play into the drawing/solving of these systems?
Oh, and this is not a trig class I'm doing. It's an...
Hello, can anyone help me with this problem?
Find an equation of the plane through P (3,3,1) that is perpendicular to the planes x +y = 2z and 2x +z =10
Thanks
The component of a force in a perpendicular direction is given by F Cos 90 and is 0.
But when one rides a bycycle and stops paddling before and after taking a 90degree turn, the bycycle continues to move forward.
What might be the explanation?
Hi,
I suppose my question has to do with planes in general, rather than just tangent planes. Say you have a plane given by the equation
z=\frac{\partial f}{\partial x}(x)+\frac{\partial f}{\partial y}(y).
How would you find the equation of the plane perpendicular to this one?
Thanks...
1. What reqiurements does a quadrangle need that all the perpendicular bisectors of the sides crosses in one point??
2. And how can you proof it?
To 1. - I think each angle have to be 90° but I can't proof it :blushing:
Kinda confused on this one becuase of the time difference involved
A train leaves a station going south at 60 km/hr at 10:00. Another train heading due west reaches this station at 11:00. The latter train was traveling at 45km/hr. At what time are they the closest?
To start with the 45...
Dear Friends,
I want to indicate a question on photons. Imagine that a photon goes in a direction and hits in a mirror to 45º. This photon is later observed like it has 90º respect its original direction.
Well, now imagine that this mirror is closed in a black box, and you don't know...
Hello,
Please bear with me...my brain is in vapor lock.
I have a line L1 given by the following parametric equations:
x = 2+3t, y = -1+5t, z = 8+2t
I need to find the equation of a line L2 passing through point B = (1,2,5) and perpendicular to L1.
For the life of my tired, worn...
I have been struggling with this question for a little while now and after drawing pictures and such I just cannot think of a situation in which this is possible. I was wondering if somebody with a little bit more physics knowledge could enlighten me :rolleyes: ? Here it is:
"Describe a...
hello,
Sorry to ask this question again, but I am having a little trouble with it still. I found a pic on a website that should be helpful.
According to my physics text, the electric field has to emerge perpendicular from the surface. I can see how this is true. Since the surface is at...
I am having trouble understanding a question to a
volume problem.
The base of a solid S is a circle of radius two in the
xy plane centered at the origin. Cross-sections of
the solid perpendicular to the base are squares.
I am thinking y = 4-X^2. Where do I find the
shape for the...
If you had two vectors, and you wanted to find a vector perpendicular to those useing th dot product, what would be needed to be done. I alreaded Doted A *dot* B and have a vector. I'm just stuck on the last part
Got a question "Find an equation of the straight line which passes through the origin and is perpendicular to the line y = 1/2x + 3.
Is the origin (0,0)?
I feel stupid!
Thanks in advance.
Does anyone know anything about perpendicular functions? I just kinda stumbled onto it thinking about perpendicular tanget lines. Could anyone shed light on the situation?
Got a problem which should be easy but having trouble...
"Find the equation of the tangent plane to z=f(x,y)=x^2 + y^2 - 1 at point (1,1,1)
"Find an equation to a plane that is perpendicular to that tangent plane and also passes through the point (1,1,1)
Thanks!
Does this concept is connected with a pure geometry (of space)?.
Thus each dimension is perpendicular at all another.
It is simple for presenting graphically up to three dimensions:
point, line, square, cube and …..
Further it is much more difficult. What a physical sense of...
If you have a 3d vector, how do you find out the perpendicular vector to this (the normal plane and stuff)? I know that the scalar product has to be 0, but surely that leaves hundreds of ones that would do that, as 2 of the 3 numbers can be chosen and the last one changes the value to 0.
Excerpt from:
Beicher and Serway, "Physics for Scientists and Engineers with
Modern Physics, 5th edition"
Chapter 24, problem 58, part c:
Two infinite, non conducting sheets of charge are parallel to each other, as show in the figure. The sheet on the left has a uniform...