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What else can I help you with?
What is a line of characteristics?
shortest distance between two points in space
How do you prove the shortest line between two points is the segment that joins them on a plane?
The shortest line between two points is NOT always the segment that joins (or jion) them on a plane: the answer depends on the concept of distance or the metric used for the space. If using a taxicab or Manhattan metric it is the sum of the North-South distance and the East-West distance. There are many other possible metrics.The proof for a general metric is the Cauchy-Schwartz inequality but this site is totally incapable of dealing with the mathematical symbols required to prove it.
The shortest path from a starting point to an endpoint what is it called?
The shortest path between two points is called a geodesic. In flat (Euclidean) space it is simply a straight line.
The straight line distance between any two points?
this is supposedly the shortest distance between any 2 points, however if you could bend the space between the two points and fold them together, well then they would be right beside each other
Given two points A and B in the three dimensional space what is the set of points equidistant from A and B?
A plane is the set of all points in 3-D space equidistant from two points, A and B. If it will help to see it, the set of all points in a plane that are equidistant from points A and B in the plane will be a line. Extend that thinking off the plane and you'll have another plane perpendicular to the original plane, the one with A and B in it. And the question specified that A and B were in 3-D space. Another way to look at is to look at a line segment between A and B. Find the midpoint of that line segment, and then draw a plane perpendicular to the line segment, specifying that that plane also includes the midpoint of the line segment AB. Same thing. The set of all points that make up that plane will be equidistant from A and B. At the risk of running it into the ground, given a line segment AB, if the line segment is bisected by a plane perpendicular to the line segment, it (the plane) will contain the set of all points equidistant from A and B.
What is the amount of space between two points?
Amount of space between two Points
What is the longest line segment?
The longest line segment is theoretically infinite, as a line segment can extend indefinitely in either direction. However, in practical terms, the longest line segment within a defined space, such as a circle, is the diameter, which is the longest distance between any two points on the circumference. In a three-dimensional space, the longest line segment would be the diagonal across a given volume, like the diagonal of a cube, which can be calculated using the Pythagorean theorem.
Can the displacment vector for a particle moving in two directions ever be longer than the length thraveled by the particle?
In a Euclidean space, the shortest distance between two points is a straight line, so no.
How can the shortest distance between two points be a curve?
Actually, this turns out to be more of a debate than you might think. Historically, most of us were taught the shortest distance between two points is a straight line; that is a principle of Euclid's geometry. But not everyone agrees with Euclid, and there are other types of geometry. For example, because the Earth is a sphere, and not flat as distance maps portray it, that is why some scientists say that the shortest distance is actually a sphere or a curve (in other words, the distance would be measured by following the Earth's contours).
What is distance between 2 points science?
The distance between two points is the shortest path connecting them in a straight line. In mathematics, you can calculate it using the distance formula, which involves the coordinates of the two points. In physics, distance can also refer to the physical separation between two objects or locations.
What determines the distance between two points?
The distance between two points is determined by the straight line that connects them, often calculated using the Euclidean distance formula. In a two-dimensional space, this distance can be computed using the coordinates of the points with the formula: (d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}). In three-dimensional space, the formula extends to include the z-coordinates as well. Essentially, the distance is a measure of the shortest path between those points in a given coordinate system.
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.
