Finding Distances to Lines and Planes in 3D Geometry

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In summary, the conversation discusses finding the distance from a point to a line, the distance between a point and a plane, and the principle unit normal, curvature, and radius of curvature for a plane curve. The conversation also mentions using formulas for distance and finding lines perpendicular to given points and planes.
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mercedesbenz
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Homework Statement


1. please help me find the distance from the point (0, 0 ,0) to the line
[tex]x=4-t, y=3+2t, z=-5+3t (-\nfty<t<\infty)[/tex]

2. find the distance between the point (3, 1, -2) and the plane [tex]x+2y-2z=4[/tex]

3 find the principle unit notmal N, the curvature , and the radius of curvature for the plane curve [tex]r(t)=ti+(sint)j[/tex]


Homework Equations





The Attempt at a Solution

 
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  • #2
Show your attempt.
 
  • #3
If we won't even try, we have no idea what methods would be appropriate!

Most calculus textbooks give FORMULAS for "distance to a line" and "distance to a plane". Can you use them?

Do you know how to find the line, through a point, perpendicular to a given point?

Do you know how to find the line, through a point, perpendicular to a given plane?

Do you understand why those would be useful for this problem?
 

1. What is a point?

A point is a location in space that has no size or dimension. It is often represented by a dot and can be described by its coordinates, which indicate its position along the x, y, and z axes.

2. How is a line defined?

A line is a straight path that extends infinitely in both directions. It is defined by two points and can be represented by a line segment with an arrow on each end to indicate its infinite nature.

3. How is distance measured between a point and a line?

The distance between a point and a line is the shortest distance between the two. It can be measured by drawing a perpendicular line from the point to the line and finding the length of that line.

4. Can a point be on a line?

Yes, a point can be on a line. In fact, a line is made up of an infinite number of points.

5. How is distance calculated between two points?

The distance between two points is calculated using the distance formula, which is the square root of the sum of the squares of the differences between the x, y, and z coordinates of the two points. It is often written as d = √[(x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2].

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