# 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.

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1. ### To find the component of a vector perpendicular to another

Problem statement : I copy and paste the (slightly different) problem statement as it appeared in the text to the right. Attempt : By inspection, we find that the vector ##\vec B'## perpendicular to ##\vec B = 3\hat i+4\hat j## is ##\boldsymbol{\vec B' = 4\hat i -3\hat j}##, remembering that...
2. ### Magnetic field force between two perpendicular wires

There are a couple of problems with the same setup. On plugging in the values and solving for the integral, I am not getting the expected values of the force. Is there something wrong in the solution attached?
3. ### Rotational inertia of square about axis perpendicular to its plane

For this problem, How do we calculate the moment of inertia of (2) and (3)? For (3) I have tried, ##I_z = \int r^2 \, dm ## ## ds = r ## ##d\theta ## ##\lambda = \frac {dm}{ds}## ##\lambda ## ##ds = dm ## ## \lambda r ## ##d\theta = dm ## ##I_z = \lambda \int r^3 d\theta ## ##I_z = \lambda...
4. ### I Does the aerial [antenna] not need to be positioned perpendicular?

Shouldnt the aerial be in perpendicular orientation for all em waves? including radio

29. ### Finding a Mistake in My Sketch: Can I Get Emergent Beam Perpendicular to AB?

This is my sketch: I think the only possible way to get emergent beam perpendicular to AB is when the incoming ray is refracted towards side AC then total internal reflection occurs as shown in my sketch. Angle QAR = 60o and angle ARQ = 90o so angle AQR = 30o It means angle CQP is also 30o...
30. ### Why is lift perpendicular to the wing?

It is said that lift on a wing always acts perpendicular to the relative wind. Why is this so? Is it because we arbitrarily choose to analyze its components with one purposely chosen to be perpendicular or is it a matter of physics that the lift component is naturally perpendicular. If so...
31. ### Motion under a force perpendicular to the velocity

I think i could deal with this problem interpreting this force like a central force, what seems pretty nice to me, since in a circular orbit the force will always pass through the center, if it is perpendicular to the velocity. I thought, since the force is central and in this case, spherically...
32. ### Non-circular motion of a particle in a perpendicular constant magnetic field

There's a constant magnetic field B. If a particle is acted on by a force qv*B (* cross) only, and the initial velocity v0 is normal to B, is the motion certainly a circular one (for any m, q, v0)? mv''=qv*B If one solves this equation (vector), it doesn't seem obvious.
33. ### Silly question -- Perpendicular forces have no effect on speed?

If route perpendicullar forces supose to have no affect, why isn't this the case when somebody tries to cross a river? the motion is perpendicullar when water speeds aprox. at the same direction.. what am i missing?
34. ### B Do Perpendicular Velocities Affect Relative Motion?

Let's say we have two people that travel with respect to each, other in some inertial frame. So if we took the relative velocity of them will they be the same in as v^12+v2^2
35. ### Why a force perpendicular to the velocity doesn't change the magnitude?

As I have shown in the picture even if their is minimal change but shouldn't it increase after a long time as minimal changes will keep accumulating.
36. ### MHB Finding lines through given point perpendicular and parallel to given line

Hey, not sure how to translate this from my native language, I hope you understand what I mean. Write down for the line y = 2x + 3 perpendicular and parallel lines passing through the point (1; 1) equations.
37. ### Perpendicular forces acting in x and y directions

Hi everyone! So I got a question shown below here and I’m struggling in what the question is trying to say here and what it wants me to give? Here is what I done For when resolving the individual x and y component of forces, my angle has always been measured counter clockwise from the...
38. ### Force between two perpendicular wires

μThe magnetic field is supposed to be B=μ0i/(2πr). I think that the force would be aimed upwards. Now I tried to divide the wire BC to infinite smaller wires where B is roughly constant in each one of them. What I get is: However this is not correct when I plug the relevant numbers in it...
39. ### Which force acts perpendicular to the side faces of an axe head?

Say that these pictures are accurate. Personally, I think I can solve this problem, but the issue is, that I had a debate on it with my Physics teacher. This is how my teacher would solve it; my teacher says that each Fk on each side is constructed from half of F and Fx. So, F = 2 * Fk * sin...
40. ### Minimum distance between two perpendicular moving vehicles

Below is my solution, which I'm not sure is correct. Hopefully the picture shows clearly what I'm trying to find.
41. ### Why must the x and y axis be perpendicular?

Homework Statement I have a conceptual question regarding why the x and y-axis must be perpendicular. Chapter 2 in section 2-1 of Giancoli's Physics states that " The x and y axes are always perpendicular". This chapter is one-dimensional motion and the section is Reference frames and...
42. ### I Do two perpendicular wires exert a force on each other?

I have a question for my E&M assignment (I'm not putting it in the homework thread since I just need more of a concept check) that involves a straight wire with current through it. If you have a wire with a current through it, and you have a rectangular wire also with current, to the right of...
43. ### Equation of a plane perpendicular to another plane

Hi, I am really stuck! I need to find the equation of the plane through the line x=2y=3z perpendicular to the plan 5x+4y-3z=8. Can anyone give me any pointers of where to start with this? Not expecting a full solution, just an idea of where to start. THanks!
44. ### I Problem with gravitation field perpendicular vector.

since it is known that ##\vec{A_\perp} = -{mG \over R^2}## why did the professor write it as ##\vec{A_\perp} = {- R G \rho \over 3}## for perfect sphere with perfect mass distribution ? Shouldn't it be ##\vec{A_\perp} = -{4 \over 3} \pi R G \rho##? I need help thanks.
45. ### Moment of inertia about a perpendicular axis through its center?

Homework Statement A 15-cm-diameter CD has a mass of 21 g . What is the CD's moment of inertia for rotation about a perpendicular axis through its center?Homework Equations I = (1/2)MR^2 3. The Attempt at a Solution I = (1/2)(0.21g).((15/2)^2) = 5.9*10^-4 kg*m^2 cant see what I am...
46. ### MHB Perpendicular Bisector: Understanding the Wording

I know that when two lines are perpendicular their gradients multiply to -1 but I don't get the wording here. Any suggestions?
47. ### MHB Find the equation of the line through (-9, 2); perpendicular to y= -1

Find the equation of the line through (-9, 2); perpendicular to y= -1. Use standard form : y=mx+b
48. ### B How to calculate a perpendicular line?

Hi, i get the math that is involved but if I have only the x,y coordinates for 2 points to connect and if i want to know what will be the perpendicular line to the line connecting these two points, how can I do that?
49. ### B Addition of Perpendicular Vectors in two ways

I have a Force Vector = 100N, making an Angle = 45 degrees with x-axis. When I find their Components trigonometrically, I get 70N each; as Fx = 100xCos(45) = 70N Fy = 100xSin(45) = 70N Verifying the result, by Head-to-Tail method, I get 70N + 70N = 140N. Why is there discrepancy or where am I...
50. ### I People pulling rope, one in a perpendicular direction

Let's say that we have two guys, each weighs 50 kg. They are pulling a piece of against each other as hard as they can. The tension of the rope will therefore be the force of friction acting on each of them (the same magnitude). Now, let's say that a third person joins the party and grabs the...