3D Vector Geometry

GeoGebra Institute of MEI, Jan 24, 2018

Table of Contents

  1. Vector equation of a line
    1. Vector equation of a line in 3D
  2. Shortest distance between skew lines
    1. Skew lines: finding the distance (dot product)
    2. Skew lines: finding the distance (cross product)
  3. Orientation of three planes
    1. 3 planes: unique point of intersection
    2. 3 planes: 2 parallel
    3. 3 planes: 3 parallel
    4. 3 planes: prism
    5. 3 planes: sheaf

1.

Vector equation of a line

  • 1. Vector equation of a line in 3D

1.1.

Vector equation of a line in 3D

– GeoGebra Institute of MEI

2.

Shortest distance between skew lines

  • 1. Skew lines: finding the distance (dot product)
  • 2. Skew lines: finding the distance (cross product)

2.1.

Skew lines: finding the distance (dot product)

Use the sliders to find the values of [math]\lambda[/math] and [math]\mu[/math] such that the vector PQ is perpendicular to both lines.
– GeoGebra Institute of MEI

2.2.

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3.

Orientation of three planes

  • 1. 3 planes: unique point of intersection
  • 2. 3 planes: 2 parallel
  • 3. 3 planes: 3 parallel
  • 4. 3 planes: prism
  • 5. 3 planes: sheaf

3.1.

3 planes: unique point of intersection

– GeoGebra Institute of MEI

3.2.

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3.3.

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3.4.

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3.5.

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