MEI Tasks for FM (8) – Vectors: Intersection of 3 planes

GeoGebra Institute of MEI, Jan 11, 2021

Intersection of 3 planes task


  • 1. (a) Intersection of 3 planes: example 1
  • 2. (b) Intersection of 3 planes: example 2
  • 3. (c) (i) 2 parallel planes
  • 4. (c) (ii) 3 parallel planes
  • 5. (c) (iii) Sheaf of planes
  • 6. (c) (iv) Prism of planes
  • 7. (Extension) The equation of a plane in 3D

1.

(a) Intersection of 3 planes: example 1

[list=1][*]Plot the planes with equations:[br][b]x−2y+4z=4[br]x+y−z=2[br]x+3y+z=6[/b][br][br][/*][*]Select [b]Tools[/b] in the left-hand panel and use the [b]Intersect two surfaces[/b] tool to find the line of intersection of two of the planes.[br][br][/*][*]Use the [b]Intersect two surfaces[/b] tool again to find the line of intersection a different pair of planes.[br][br][/*][*]Select [b]More [/b]and use the [b]Intersect[/b] tool to find the point of intersection of these lines. [br][br][/*][*]Select [b]Algebra[/b] in the left-hand panel to view the point of intersection.[br][/*][/list]
What are the coordinates of the point of intersection?
How can you use a matrix to find the point of intersection of 3 planes?
– GeoGebra Institute of MEI

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