Do these 3D vectors intersect at the given points?

  • Thread starter paulfr
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In summary, the conversation discusses using Wolframalpha to find the solution for two lines with equations x=1+2t, y=2-t, z=t and x=-2-s, y=3+3s, z=1+4s. The solution given by Wolframalpha is t=-8/5 and s=1/5, but the z values do not match. The speaker uses matrix methods to show that the lines do not intersect and questions if there is a subtle interpretation being made by Wolframalpha. They also mention that the lines appear skew.
  • #1
paulfr
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If I put these 2 lines into wolframalpha.com it comes up with a solution

x = 1 + 2t , y = 2 – t , z = t ; x = -2 – s , y = 3 + 3s , z = 1 + 4s

t = -8/5 and s = 1/5 using equations for x & y

Solution; x = -11/5 y = 18/5 z = 9/5But the z values do not match so how can these lines intersect ?

Thanks for your input
 
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  • #2
Setting the x, y, and z values equal, you get the system of equations
1 + 2t = -2 - s
2 - t = 3 + 3s
t = 1 + 4s

Moving the variables to one side gives this system
s + 2t = -3
3s + t = -1
4s - t = -1

Using matrix methods, this turns out to be an inconsistent system, meaning that the two lines don't intersect. Are you sure that the equations you entered into wolframalpha are the same as you posted?
 
  • #3
Yes I checked the data several times
Wolframalpha's solution seems to ignore that z=t which
gives a different value than the 9/5 from z=1+4s

Perhaps there is some subtle interpretation they are making ?

The lines appear skew to me

Thanks for the comments
 

What is 3D Vector Inconsistency?

3D Vector Inconsistency is a problem that occurs when the mathematical calculations performed on 3D vectors do not produce consistent results. This can happen due to errors in data input, rounding errors, or improper use of vector operations.

What are some common causes of 3D Vector Inconsistency?

Some common causes of 3D Vector Inconsistency include using incorrect vector operations, using vectors with different dimensions, and using vectors with incorrect magnitude or direction.

How can 3D Vector Inconsistency be avoided?

To avoid 3D Vector Inconsistency, it is important to use proper vector operations and ensure that all vectors being used have the same dimensions and correct magnitudes and directions. Additionally, double-checking data input and performing checks for rounding errors can also help prevent this issue.

What are the consequences of 3D Vector Inconsistency?

The consequences of 3D Vector Inconsistency can range from minor errors in calculations to significant inaccuracies in results. This can lead to incorrect conclusions and potentially impact the validity of a scientific study or project.

How can 3D Vector Inconsistency be detected and corrected?

3D Vector Inconsistency can be detected by performing checks on the results of vector operations and comparing them to expected values. If inconsistencies are found, they can be corrected by identifying the source of the inconsistency and making necessary adjustments, such as using more accurate data or selecting a different vector operation.

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