Determining wheter point lie on line

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Discussion Overview

The discussion revolves around determining whether the points (5, -6, 10) and (3, 3, 8) lie on a specified line defined by the parametric equations x = 2 + t, y = 3 - 3t, z = 4 + 2t. The scope includes mathematical reasoning and problem-solving related to vector equations.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Debate/contested

Main Points Raised

  • Some participants suggest finding a value of t such that the coordinates of the points match the parametric equations of the line.
  • One participant proposes an alternative parametric equation for the points (5, -6, 10) and argues that it does not match the given line's equations.
  • Another participant questions the clarity of the problem statement and emphasizes the need to solve the vectorial equation presented in the initial post.

Areas of Agreement / Disagreement

Participants express differing views on whether the points lie on the line, with some proposing methods to verify this and others questioning the approach taken. The discussion remains unresolved regarding the relationship of the points to the line.

Contextual Notes

There are unresolved assumptions regarding the interpretation of the problem and the methods used to analyze the points in relation to the line.

salistoun
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Hi all,

How do I go about solving the following question?

Determine whether the points (5 , -6 , 10) and (3, 3 , 8) are on the line
x = 2 + t; y = 3 - 3t, z = 4 + 2t

Stephen
 
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salistoun said:
Hi all,

How do I go about solving the following question?

Determine whether the points (5 , -6 , 10) and (3, 3 , 8) are on the line
x = 2 + t; y = 3 - 3t, z = 4 + 2t

Stephen

Just find out whether there exists a value [itex]\,t\in\Bbb R\,[/itex] s.t. [itex]\,(5,-6,10)=(2+t,3-3t,4+2t)\,[/itex] , and the same with the other vector...

DonAntonio
 
Hi Don,

If I'm correct, the parametric equation for the following points is:

x = -2t + 5, y = -9t - 6 and z = -2t + 10

So no values are matching this parametric
x = 2 + t; y = 3 - 3t, z = 4 + 2t.

So therefore it does not lie on the line right?
 
salistoun said:
Hi Don,

If I'm correct, the parametric equation for the following points is:

x = -2t + 5, y = -9t - 6 and z = -2t + 10

So no values are matching this parametric
x = 2 + t; y = 3 - 3t, z = 4 + 2t.

So therefore it does not lie on the line right?

What is "the following point"? The point is given to you: (5,-6,10), period. You only have to solve the easy vectorial equation I wrote in my first post.

DonAntonio
 
Thanks Don i do get what u saying
 

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