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In plane geometry it is a straight line. If you want to know the shortest line between two points on a globe, it will be the intervening section or arc of the great circle route that connects the points. The great circle will be a circle that cuts the globe into exactly equal parts, like the equator.
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Through any three points not on a line there is one?
between two point there is exactly one line between three points there is exactly one plane
What is the curved line between any two points on a circle?
an arc
What is directed-line segment?
is a segment of the line consisting of any two points and the part between
If a line had a series of five or six points could the outer two most points be considered a line segment?
"Points" are never considered a line segment. Points are never anything else but points.But any two points 'determine' a line segment, because there's only one line segmentthat can be drawn between them.So if you have several points on a line, then any two of them determine a segmentof that line.
If the shortest distance between two points is a straight line what is the shortest distance between two straight lines?
The question is curiously vague. Do the two lines exist in the same plane? If they do, then they must intersect somewhere -- unless they are parallel. For non-parallel lines, the distance between the two lines at the point of intersection is zero. For parallel lines, the shortest distance between them is the length of the line segment that is perpendicular to both. For intersecting lines, there is an infinite number of distances between the infinite number of pairs of points on the lines. But for any pair of points -- one point on line A and another on line B -- the shortest distance between them will still be a straight line. Given two lines in 3D (space) there are four possibilities # the lines are collinear (they overlap) # the lines intersect at one point # the lines are parallel # the lines are skew (not parallel and not intersecting) The question of "shortest distance" is only interesting in the skew case. Let's say p0 and p1 are points on the lines L0 and L1, respectively. Also d0 and d1 are the direction vectors of L0 and L1, respectively. The shortest distance is (p0 - p1) * , in which * is dot product, and is the normalized cross product. The point on L0 that is nearest to L1 is p0 + d0(((p1 - p0) * k) / (d0 * k)), in which k is d1 x d0 x d1.
