Perpendicular lines Definition and 19 Threads

In ##\mathbb{R}^2##, there are two lines passing through the origin that are perpendicular to each other. The orientation of one of the lines with respect to ##x##-axis is ##\psi \in [0, \pi]##, where ##\psi## is uniformly distributed in ##[0, \pi]##. Also, there are two vectors in...

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?

Homework Statement find the shortest distance from (0,0) to the line passing A(2,3) and B(3,5) Homework Equations ## \frac{y-y1}{y2-y1} = \frac{x-x1}{x2-x1} ## y-y1 = m (x-x1) m1 * m2 = -1 (m1 perpendicular to m2) The Attempt at a Solution line passing A and B points ## \frac{y-3}{5-3} ## =...

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...

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...

Hi all, When you have a surface defined by F(x, y, z) = 0 where x = f(t), y= g(t) and z= h(t) and a point on this surface P_0 = (x_0, y_0, z_0) , could someone explain to me why a line through P_0 with direction numbers [\frac{dx}{dt}, \frac{dy}{dt}, \frac{dz}{dt}] is perpendicular to a...

As students taking pre-calculus, you are probably aware that when two lines are perpendicular, the product of their slopes is -1. Let's see why this is. Let one line be $\displaystyle y_1=m_1x+b_1$ and the other line be $\displaystyle y_2=m_2x+b_2$. Now,we know the angle of inclination of a...

Homework Statement ABCD is a quadrilateral with AB=CD P,Q,R,S are the midpoints of AD,AC,BD,BC respectively Prove that PS is perpendicular to QR Homework Equations The Attempt at a Solution I've tried a bunch of different avenues, but I think that the most promising one is...

Homework Statement what is the relation between complex slopes of two perpendicular lines?? :think: Homework Equations The Attempt at a Solution i think it is same as the slopes of two st. lines that is the product shud be -1...but the answer given is sum of slopes is 0...

Homework Statement Suppose T is a Mobius map take Real -> Real and infinite infinitely to 0 a) What's the image of the family of lines parallel to Real? b) What's the image of the family of lines perpendicular to Real? c) Show the Mobius map take D = {z :|z|<1} onto itself iff Tz =...

A very simple and noob question, sorry for this. Looking at http://en.wikipedia.org/wiki/Perpendicular I found that two lines are perpendicular if and only if the product of their slopes is -1. If I have two lines described by the following equations: y = ax + b g = cx + d then...

Homework Statement Find two straight lines that are perpendicular to y=0.25x and tangent to the curve f(x) = 1/x. Homework Equations y=0.25x f(x) = 1/x. The Attempt at a Solution What I did was equate y and f(x) and determined when they equal which is 2 and -2. The points are (2, 1/2) and...

Determine a constant real number k such that the lines AB and CD are perpendicular. A(1,2), B(4,0), C(k,2), D(1,-3). (answer given is k=-3/2) If two lines are perpendicular the product of their slopes is -1. The slope of AB is \frac{0-2}{4-1} = \frac{-2}{3} The slope of CD is...

Homework Statement Find the line through (3, 1, -2) that intersects and is perpendicular to the line x = -1 + t, y = -2 + t, z = -1 + t. Homework Equations line l through P (x1, y1, z1) and Q (x2, y2, z2) has the following form x = x1 + (x2 - x1)t y = y1 + (y2 - y1)t z = z1 + (z2 -...

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...

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...

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...

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...

Could some tell me what's the other way you could find if lines are perpendicular, other than graphing. I know another way to do it, and its algebracaly, but there's another way you could do it algebracaly too.