What is the smallest distant between 2 lines?

Question

What is the smallest distant between 2 lines?

Answer 1

Yooper is correct. If the two lines are parallel then it is the perpendicular distance. Imagine rotating the two lines so that they are both vertical, then the distance is the horizontal spacing between them. If they are not parallel, then they intersect.

The distance between the parallel lines Ax+By+C1=0 and Ax+By+C2=0 is given by |C1-C2|/sqrt(A^2+B^2).

Answer 2

it is the straight line segment that is perpendicular to both lines.

If the original two lines are not parallel then they intersect - there is no distance between them at the intersection.

Answer 3

the smallest distance is ten to the .1 infinity

Answer 4

The question is tricky, but the answer also can be.

The smallest distance between 2 lines is zero, at their intersection.

This I can say for sure, for truth and forever, and it is unquestionable.

Answer 5

Assuming the lines are parallel or not in the same plane (that is, the lines do not cross), then the smallest distance is the Planck length, or about 1.616 x 10^-35 meters. In quantum physics, distance is quantized like any other physical attribute, and the Planck length is the smallest possible unit of distance that can be measured. That is, if the distance were less than the Planck length, it would be impossible to measure. Not just practically impossible, but theoretically impossible.

Answer 6

when two lines become one

Answer 7

1} If they are parallel, it is the straight line segment that is perpendicular to both lines. The shortest distance which can be possible is the Planck length, or about 1.616 x 10^-35 meters. In quantum physics, distance is quantized like any other physical attribute, and the Planck length is the smallest possible unit of distance that can be measured. That is, if the distance were less than the Planck length, it would be impossible to measure. Not just practically impossible, but theoretically impossible.

2}If the original two lines are not parallel then they intersect - there is no distance between them at the intersection.

By the way, I would like to point out that two lines will always be co-planar {i.e., the will lie in the same plane}.