Perpendicular Lines in Three Space

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Discussion Overview

The discussion revolves around finding the equation of a line L2 that passes through a specific point and is perpendicular to another line L1 defined by parametric equations. The focus is on the mathematical reasoning involved in determining the direction numbers for L2 that ensure its perpendicularity to L1.

Discussion Character

  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • One participant presents the parametric equations of line L1 and seeks help in finding the direction numbers for line L2 that would make it perpendicular to L1.
  • Another participant suggests that any vector (x, y, z) satisfying the dot product condition with the direction numbers of L1 will be perpendicular to L1.
  • A participant identifies multiple potential solutions for the direction numbers of L2, expressing uncertainty about how to determine which solution is correct.
  • Another reply confirms that any of the proposed direction numbers would work and suggests picking one to find the intercepts.

Areas of Agreement / Disagreement

Participants express agreement on the method for finding perpendicular direction numbers, but there is no consensus on which specific solution to choose from the multiple options provided.

Contextual Notes

The discussion includes various proposed direction numbers for L2, but the criteria for selecting the most appropriate one remain unresolved. There is also a lack of clarity on the implications of each choice regarding the intercepts.

Who May Find This Useful

Readers interested in vector mathematics, particularly in the context of geometry in three-dimensional space, may find this discussion relevant.

dogma
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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 out brain...I cannot figure out how to determine the direction numbers that would make L2 perpendicular to L1 (with direction numbers (3,5,2)).

Can someone please give my brain a kick start.

Thanks a bunch.

dogma
 
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Any vector [itex](x, y, z)[/itex] such that [itex](3, 5, 2) \circ (x, y, z) = 0[/itex] has direction perpendicular to that of your line.
 
Last edited:
That makes sense, but I can see a couple of soulutions to that:

(a,b,c) = (1,-1,1), (-1,1,-1),(1,-3,6),...

If I'm on the right track, how do I determine which is correct?

Thanks again.
 
dogma said:
That makes sense, but I can see a couple of soulutions to that:

(a,b,c) = (1,-1,1), (-1,1,-1),(1,-3,6),...

If I'm on the right track, how do I determine which is correct?

Thanks again.

Any of those would work. Pick one and figure out the intercepts.
 
okay, my brain is starting to show some activity...thanks all

dogma
 

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