Equidistant Points from P & Q in 3D Space

Thread starter Reeses
Start date Nov 19, 2008
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3d Vectors

In summary, "equidistant points from P & Q in 3D space" refers to a set of points that are all the same distance from two given points, P and Q, in a three-dimensional coordinate system. To determine these points, one would first find the midpoint between P and Q and then use the distance formula to calculate the distance from the midpoint to any other point. These points can have various practical applications, such as locating a point equidistant from two objects or finding the center of a circle passing through P and Q. There can be multiple sets of equidistant points from P and Q, as there are an infinite number of points that can satisfy this condition. Additionally, the concept of equidistant points

Nov 19, 2008

Reeses

Let P=(–5,7,6) and Q=(–6,–4,2). The set of all points that are equidistant from P and Q has the equation=?

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Nov 19, 2008

Mark44

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What have you tried?

If you haven't tried anything, you might start with a point (x, y, z) that is one of the set of points equidistant from the two given points. Do you know a formula for distance in 3-D space?

Related to Equidistant Points from P & Q in 3D Space

1. What is the definition of "equidistant points from P & Q in 3D space"?

"Equidistant points from P & Q in 3D space" refers to a set of points that are all the same distance from two given points, P and Q, in a three-dimensional coordinate system.

2. How do you determine the equidistant points from P & Q in 3D space?

To determine the equidistant points from P & Q in 3D space, you would first need to find the midpoint between P and Q. Then, using the distance formula, you can find the distance from the midpoint to any other point in the coordinate system. The points that have the same distance from the midpoint as P and Q are the equidistant points.

3. What is the significance of finding equidistant points from P & Q in 3D space?

Finding equidistant points from P & Q in 3D space can be useful in various applications, such as determining the location of a point that is equidistant from two objects (P and Q) or finding the center of a circle that passes through P and Q.

4. Can there be more than one set of equidistant points from P & Q in 3D space?

Yes, there can be more than one set of equidistant points from P & Q in 3D space. This is because there are an infinite number of points that can be equidistant from two given points in a three-dimensional coordinate system.

5. How does the concept of equidistant points from P & Q in 3D space relate to symmetry?

The concept of equidistant points from P & Q in 3D space is closely related to symmetry. In fact, the equidistant points can be seen as the points of symmetry between P and Q, as they are all the same distance from both points. This can be visualized as a mirror image or reflection of P and Q across the equidistant points.