WildLinAlg10: Equations of lines and planes in 3D

This video shows how we work with lines in the plane and planes in 3D space in Linear Algebra. A line in 2D is represented by a linear equation in x and y, a plane in 3D by a linear equation in x,y and z. Both can also be described in parametric form. It is important to be able to change from a Cartesian to a parametric form.

The space of all lines in the plane has a curious connection with the Mobius band. Lines in 3D are somewhat trickier to describe since they require two linear equations.

This is the tenth video in a first course of Linear Algebra given by N J Wildberger of the School of Mathematics and Statistics at UNSW. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry---see his WildTrig YouTube series under user `njwildberger'. There you can also find his series on Algebraic Topology, History of Mathematics and Universal Hyperbolic Geometry.

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[MrFunatabi]

Hi professor,

What is the geometric interpretation of the case where Δ = 0 if we use z = λ? It's on slide 15 around 55:00. Thanks!

[UNSWelearning]

Hi MrFunatabi The geometrical interpretation is that the intersection of the two planes that we started with is actually parallel to the xy plane. So it does not meet any plane z=lambda (which is a plane also parallel to the xy plane) in a unique point.

[theNewCodingFrontier]

haha, I love how odd professors can be. Example, drum stick pointer.

[UNSWelearning]

Hi theNewCodingFrontier

What's odd about a drum stick? Has a certain practical utility. And of course it rocks and rolls...

[sekwah09]

Great video lecture and fantastic teacher, very clear, concise, easy to follow examples, thanks for posting

[osmannee]

Branislav Stojanovic is that You

[harryprer]

hello professor, what is the geometrical interpretation of a plane?

[userisdosser]

Its very hard to imagine 3d...

anyway Thanks prof..

[haydonism]

hey man, thanks a lot for these videos! i'm trying to teach myself a further maths alevel and this helps enormously!