3D Vectors

MrYardley, Oct 3, 2023

Explaining all the concepts needed in 3D vectors to aid in visualisation and problem solving.

Table of Contents

  1. Lines in 3D
    1. Equation of a Line in 3D
    2. Intersections
    3. Distances
    4. Angles
    5. Applications
  2. Planes
    1. Equations of Planes
    2. Lines and Planes
    3. Distances
    4. Angles
    5. Problem Solving
    6. Intersecting Planes

1.

Lines in 3D

  • 1. Equation of a Line in 3D
  • 2. Intersections
  • 3. Distances
  • 4. Angles
  • 5. Applications

1.1.

Equation of a Line in 3D

What is the minimum amount of information needed to find the equation of a line in 3D?
– MrYardley

1.2.

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1.3.

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1.4.

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1.5.

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2.

Planes

  • 1. Equations of Planes
  • 2. Lines and Planes
  • 3. Distances
  • 4. Angles
  • 5. Problem Solving
  • 6. Intersecting Planes

2.1.

Equations of Planes

Use the geogebra file below to help with this task. There are ready made points and vectors, which you can edit to fit the information in the question.[br]For part c) make sure you show the line and then the plane you have found.
What information is needed in order to find the equation of the plane?
– MrYardley

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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Information