Register to reply

Directed distance to a directed line

by Baba-k
Tags: directed, distance, line
Share this thread:
Mar13-11, 10:06 AM
P: 9

I've reached a question in a maths text book I'm reading that I'm having some trouble with. Any help/suggestion would be greatly appreciated. The question it self is short but there are a couple of paragraphs which set it up that I've copied directly out of the book.

1. The problem statement, all variables and given/known data
We distinguish a positive and a negative side of a directed line l as follows. Let P be any point not on l, and let Q be the foot of the perpendicular to l through P. Then P is on the positive or negative side of l according as the angle from l to the directed line QP is 90 or -90 degrees.
We shall now determine the equation of a directed line l. We draw through the orign O a line m perpendicular to l, and direct m so that the angle from it to l is 90 degrees. The angle from the directed x-axis to m will be called [tex]\beta[/tex]. Then [tex]\alpha = 90^{\circ} + \beta , \sin \alpha = \cos \beta , cos\alpha = -\sin \beta[/tex]. Let R with coordinates x1, y1 be the point where m meets l. We shall denote by d the directed distance OR on directed m.

Show that d is positive if and only if O lies on the negative side of l.

2. Relevant equations

3. The attempt at a solution
The question states that d should be positive if and only if O is on the negative side of l. However I've attached a simple sketch where (i think) d is positive when O is on the positive side (the black line being l and the green one being d and m). I'm not sure what I've done wrong to get this result, any pointers would be great :)

thanks alot
Attached Thumbnails
Phys.Org News Partner Science news on
'Office life' of bacteria may be their weak spot
Lunar explorers will walk at higher speeds than thought
Philips introduces BlueTouch, PulseRelief control for pain relief

Register to reply

Related Discussions
Directed graphs Calculus & Beyond Homework 0
Directed EMF Generator? Electrical Engineering 6
Force Vector Directed Along A Line Introductory Physics Homework 1
Need help with 3D vector; force directed along a line Introductory Physics Homework 30
Directed sets Calculus & Beyond Homework 3