Perpendicular Line Equations for Skew Lines in Different Planes

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In summary, the conversation is about finding equations for a line that is perpendicular to two given lines. The lines are skew and the method of finding the direction vectors is discussed. The conversation also mentions the need for a textbook and the use of cross products. The final solution involves fixing constants to ensure the perpendicular line intersects the other two lines.
  • #1
Iyafrady
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Homework Statement


Find equations for a line perpendicular to both of these lines.

Homework Equations


(x/3)=(y/2)=(z/2) and (x/5)=(y/3)=(z-4)/2

The Attempt at a Solution



i don't know how to start?I know the two lines are skew, if i take the cross product will it be perp. to both lines??Can i take the cross product of two lines that lie in different planes?
 
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  • #2
You don't take the cross product of the lines. You take the cross product of the direction vectors of the lines. The result is a direction vector for the perpendicular line.
 
  • #3
how do i find the direction vectors?
 
  • #4
Do you have a textbook? Isn't it covered in there?
 
  • #5
No!My book leaves a lot of details out, it expects us to know certain calculus stuff since its a post calculus course.I just don't remember direction vectors but have studied them in the past.Ill see what i can find n google.thnx anyway.
 
  • #6
Then you may need another book to keep on hand. ax=by=cz has direction vector (1/a,1/b,1/c).
 
  • #7
Hmm, i did the cross product of the direction vectors and got -2i+4J-k, but the questions asks to find the equations, i got a vector.The answer in the book is .5x-52/7=-.25y+52/21=z-208/21, they surely used another method.
 
  • #8
No. Look at the direction vector of the line they give as a solution. It's (1/.5,1/(-.25),1/1) which is (2,-4,1). You got the direction vector right. Now it looks like they want you to fix the constants by requiring that the perpendicular intersect the other two lines.
 

1. What are skew lines?

Skew lines are two lines in three-dimensional space that do not intersect and are not parallel. They are also not contained within the same plane.

2. How do you determine if two lines are skew?

To determine if two lines are skew, you can use the vector equation of the lines. If the direction vectors of the lines are not parallel and the lines do not intersect, then they are skew.

3. Can skew lines have the same equation?

No, skew lines cannot have the same equation. Since they are not parallel, they have different direction vectors and therefore cannot have the same equation.

4. How do you find the point of intersection of two skew lines?

Since skew lines do not intersect, there is no point of intersection. However, you can find the closest distance between the two lines by finding the shortest distance between any point on one line and the other line.

5. Can skew lines be in different planes?

Yes, skew lines can be in different planes. In fact, this is one of the defining characteristics of skew lines - they are not contained within the same plane.

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