My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
August 28th, 2019, 10:58 AM   #1
Newbie
 
Joined: Aug 2019
From: Denmark

Posts: 3
Thanks: 0

Calculating endpoint of 3D line with start point and angle.

So I need to calculate the start point (x1, y1, z1) of a 3D line of which I know the end point (x2, y2, z2), the angle which is 45 degrees, but where I also know y1. I furthermore know that y1<y2.

So is there a simplified formula for this, given the additional info?
ThemePark is offline  
 
August 28th, 2019, 11:04 AM   #2
Senior Member
 
Joined: Jun 2019
From: USA

Posts: 213
Thanks: 90

Which angle is 45°? You need a minimum of two angles to define a line in 3D.

Also, to find the starting point, you would need the length of the line segment (or dependent information, such as one of x1, y1, or z1).
DarnItJimImAnEngineer is offline  
September 1st, 2019, 12:04 PM   #3
Newbie
 
Joined: Aug 2019
From: Denmark

Posts: 3
Thanks: 0

English isn't my first language so I'm not sure how to describe what you ask about the angle, and I'm having a hard time wrapping my head around it all as well.

The best I can do is to provide the information that it's two points in a triangle where the third point would be (x2,y1,z2) as far as I can figure out, but like I said, I can't quite wrap my head around this so I'm not sure if that's already obvious from the previously provided info or not.
ThemePark is offline  
September 1st, 2019, 02:07 PM   #4
Senior Member
 
Joined: Jun 2019
From: USA

Posts: 213
Thanks: 90

So A = (x1,y1,z1), B = (x2,y2,z2), and C = (x2,y1,z2), where <CAB = 45° (or <ABC = 45°)? And y1 < y2.
This actually makes it easy, because everything lies in a plane perpendicular to the x-z plane.

On the other hand, if you are trying to find point A, there are actually an infinite number of solutions (all on a circle).

Let R = (y2-y1) = |BC|. We have a 45-45-90 triangle, so |AC| = |BC| = R. It is also given that the y component of A is the same as the y component of C. However, we can choose x1 and z1 any way we want, so long as |AC| = R.

So x1 = x2 + R cos(t), z1 = z2 + R sin(t),
and we can choose t to be any angle we want.
Attached Images
File Type: jpg Triangle.jpg (91.3 KB, 1 views)
DarnItJimImAnEngineer is offline  
Reply

  My Math Forum > College Math Forum > Linear Algebra

Tags
angle, calculating, endpoint, line, point, start



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Calculating the line integral of a curve given line segments nomad609 Calculus 0 October 23rd, 2016 11:39 AM
Calculating angle sin and sin angle without any functions. Gyiove Algebra 1 February 26th, 2014 04:57 PM
Drawing a line from point a,b .. coords point b unkown Vibonacci Algebra 5 September 17th, 2012 12:28 AM
Don't know where to start with compound angle question acomber Algebra 2 January 31st, 2012 06:01 AM
calculating point of line given starting point, slope mathsiseverything Algebra 1 March 4th, 2008 06:41 AM





Copyright © 2019 My Math Forum. All rights reserved.