Shortest distance between lines .

In summary, the concept of shortest distance between lines refers to the perpendicular distance between two lines without intersecting either of them. This distance is calculated by finding the vector that is perpendicular to both lines and determining the closest point on each line to this vector. This calculation is significant in many practical applications and requires the two lines to be skew and not in the same plane. The shortest distance between lines cannot be negative and is always a positive value representing the length of the perpendicular line segment connecting the two lines.
  • #1
reazreaz
2
0
shortest distance between lines...

how to find the shortest distance and the equation between the lines
(x-6)/3=(y-7)/-1=(z-4)/1 &
(x)/-3=(y+9)/2=(z-2)/4 ... pls help by solving it
 
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  • #2


This looks an awful lot like homework- in which case
1) It belongs in the homework section.
2) It wouldn't help you for some one else to solve it.


Now, first can you determine whether these lines intersect (in which case the answer is trivial), are parallel (in which case the answer is fairly easy), or are skew (in which case the answer is a little more difficult).
 
  • #3


thanks
 

FAQ: Shortest distance between lines .

What is the concept of shortest distance between lines?

The shortest distance between two lines is the perpendicular distance between them. It is the shortest distance that connects the two lines without intersecting either of them.

How is the shortest distance between lines calculated?

The shortest distance between lines is calculated by finding the vector that is perpendicular to both lines, and then finding the point on each line that is closest to this vector. The distance between these two points is the shortest distance between the lines.

What is the significance of finding the shortest distance between lines?

Finding the shortest distance between lines is important in many practical applications, such as in geometry, engineering, and navigation. It helps determine the closest distance between two objects, which can be useful in designing structures or planning routes.

What are the conditions for two lines to have a shortest distance between them?

The two lines must be skew (not parallel or intersecting) and not in the same plane. Additionally, they must not be coincident (lying on top of each other) or parallel to the same plane.

Can the shortest distance between lines be negative?

No, the shortest distance between lines cannot be negative. It is always a positive value, as it represents the length of the perpendicular line segment connecting the two lines.

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