Math Calculators, Lessons and Formulas

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Analytic geometry of three dimensions: (lesson 1 of 2)

Line in three dimensions

Equations:

Symmetric form for describing the straight line:

1. Line through line in 3 dimensions parallel to the vector (a, b, c):

line in 3 dimensions

2. Line through point Line through pointand Line through point:

Line through point

This line is parallel to the vector line parallel to the vector

Parametric Form

In three-dimensional space, the line passing through the point line parallel to the vectorand parallel to (a, b, c) has parametric equations

line example

In three-dimensional space, the line passing through the point and

line through the point

Intersection:

The line through Line Intersection in direction Line Intersectionand the line through Line Intersectionin direction Line Intersection intersect iff:

Line Intersection

Parallelism:

Three lines with directions Line Parallelismare parallel to a common plane if and only if

Line Parallelism

Distance:

Distance between the point Line point distance and the line through Line point distance in direction (a, b, c):

Line point distance

Distance between the line through Line point distance in direction Line point distance exampleand the line through Line point distancein direction Line point distance:

Line point distance