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
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
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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...
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please help
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Homework Statement
Consider the rigid body in the picture, rotating about a fixed axis z not passing through a principal axis of inertia, with an angular velocity \Omega that can vary in magnitude but not in direction. Find the angular momentum vector and its component parallel to z axis (...
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...
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Hi All,
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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
(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...
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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
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:
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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.
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Hello,
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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,
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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?
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Hello guys,
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(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...
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.
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Homework Statement
On a long dielectric line a charge with density ##10^{-3}## is applied one half with positive charge and the other half with negative charge. Perpendicular to the first line and 5 cm away from it we have another line with the same charge density and also half of it is...
The base of a solid is the region bounded by the parabola
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Each plane section perpendicular to the x-axis is square.
(I assume this means the cross-section of the solid will be square)
then we are not revolving but slicing.
The volume of the solid is? (the ans is...
Could someone explain how angular velocity points perpendicular to the plane of rotation? I mean what is a physical explanation of this? (not mathematical)
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