Finding angle between two lines

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Homework Help Overview

The discussion revolves around finding the angle between two lines represented in a non-standard form. Participants are attempting to convert the given equations into parametric or vector forms to facilitate the calculation of the angle.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are discussing how to express the given lines in parametric form and are questioning the dependencies of the variables involved. There is an exploration of different parameterizations and the implications for direction vectors.

Discussion Status

Some participants are providing guidance on how to express the equations in parametric form and discussing the nature of direction vectors. Multiple approaches to parameterization are being explored, and there is a sense of progress as participants clarify their understanding of the relationships between the variables.

Contextual Notes

There is a focus on the need for clarity in variable dependencies and the challenge of converting the original equations into a usable format for finding the angle. Participants are navigating the constraints of the problem setup without reaching a final resolution.

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Homework Statement



Two lines

x-3=2-y , z=1

x=7, y-2=z-5

Find the angle between the lines

Homework Equations





The Attempt at a Solution



The thing is that, i have no idea how to turn that into either (x,y,z) coordinates, parametric equations or vector equation. So, I really am stuck here. =/
 
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WHY can't you express them in parametric form? Choose y to be the parameter. Express the other variables in terms of y.
 
But how do you express the z term in terms of y?
 
jeffreylze said:
But how do you express the z term in terms of y?

z=1+0*y, if you want to write it that way. z doesn't have any y dependence. Nothing wrong with that.
 
oh, so it will be

x = 5-y
y
z = 1

x= 7
y
z= y+3

Hence, to find the angle, i will need two direction vectors, right? But how do i convert that into vector equation? r = ro + tv
 
I would write the first one, for example, as x=5-t, y=t, z=1. It can be a little confusing if you use the same name for the parameter as you do for the coordinate. Now you want r=(x,y,z)=(constant vector)+t*(another constant vector). Why don't you have a guess what those constant vectors might be?
 
Oh, i see. So it will be r = (5,0,1) + t*(-1,1,0) , what if i let x = t ? That will give me, r = (0,5,1) + t*(1,-1,0) . Or it doesn't matter? Because the direction vector is what I am after? Am I right here, or am I completely off track?
 
You're on track. Another possibility is r=(5,0,1)+t*(-2,2,0). I just changed t -> 2*t. It's still the same line. There are lots of ways to parametrize a line. And, yes, in any two different ways of doing it, the direction vectors will still be parallel.
 
I see. Now, it all makes sense. Thanks a lot =D
 

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