Finding Common perpendicular of two lines

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SUMMARY

The discussion focuses on finding the common perpendicular between two lines represented by the equations x / 2 = (y-1) / 2 = z and x + 1 = y – 2 = (z + 4) / 2. The user initially encounters an issue calculating the distance between the lines, resulting in a value of 0. To resolve this, the discussion suggests using the cross product to determine a vector perpendicular to the two lines, emphasizing the need to identify two specific points on each line for accurate calculations.

PREREQUISITES
  • Understanding of vector mathematics
  • Familiarity with line equations in three-dimensional space
  • Knowledge of the cross product operation
  • Basic principles of geometry related to perpendicular lines
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  • Study the method for calculating the cross product of vectors
  • Learn how to derive points from parametric equations of lines
  • Explore the concept of distance between skew lines in three-dimensional geometry
  • Investigate the geometric interpretation of perpendicular lines in 3D space
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Mathematicians, physics students, and anyone involved in vector calculus or three-dimensional geometry seeking to understand the relationship between lines and their perpendiculars.

ydan87
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Hi there,
The two given lines:
1) x / 2 = (y-1) / 2 = z
2) x + 1 = y – 2 = (z + 4) / 2
I need to find the common perpendicular between them.
Though when I tried to calculate the distance between them, I get 0.

Can someone please help?

Thanks in advance
 
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how do you find a vector that is perpendicular to two given vectors?
 
Cross product...but how would I find the two vectors?
 
ydan87 said:
Cross product...but how would I find the two vectors?

pick any two points on the same line, what about their difference?
 

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