If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:4:12

Specifying planes in three dimensions

Video transcript

we've already been exposed to points and lines now let's think about planes and you can view planes as really a flat surface that exists in three dimensions that goes off in every direction so for example if I have a flat surface like this and it's not curved and it just keeps going on and on and on in every direction now the question is how do you specify a plane well you might say well let's see let's think about a little bit could I specify a plane with one point right over here let's call that point a with that alone be able to specify a plane well there's an infinite number of planes that could go through that point I could have a plane that goes like this where that point a sits on that plane I could have a plane like that or I could have a plane like this I could have a plane like this where point a sits on it as well so I could have a plane like that and I could just keep rotating around a so one point by itself does not seem to be sufficient to define a plane well what about two points let's say I had a point B right over here well notice the way I drew this point a and B they would define a line for example they would define this line right over here so they would define they could define this line right over here but both of these points and in fact this entire line exists on both of these planes that I just drew and I could keep rotating these planes I could have a plane that looks like this I could have a plane that looks like this that both of these that both of these points actually sit on I'm essentially just rotating around this line that is defined by both of these by both of these points so two points does not seem to be sufficient let's try three so there's no way that I could put well let's be careful here so I could put a third point right over here Point C and C sits on that line and C sits on all of these planes so it doesn't seem like just a random Third Point is sufficient to define to pick out any one of these planes but what if we make the constraint that the three points are not all on the same line obviously two points can will always define a line but what if the three points are not collinear so instead of picking C is a point what if we pick what if we is there any way to pick a point D that is not on this line that is on that is on more than one of these planes well no if I say well say the point D let's say point D is right over here so it sits on this plane right over here one of the first ones that I drew so Point D sits on that plane between point D a and B there's only one plane that all three of those points sit on so a plane is defined by three non collinear points so D a and B you see do not sit on the same line a and B can sit on the same line DNA can sit on the same line D and B can sit on the same line but a B and D does not sit on they are non collinear so for example right over here in this diagram we have a plane this plane is labeled s but another way that we can specify plane s is we could say plane and we just have to find three non collinear points on that plane so we could call this plane AJ b a.j b we could call it plane g jbw plane j BW we could call it plane and I could keep going plane a wja W J a but I could not specify this plane uniquely by saying so I could not say plane plane a B W and the reason why I can't do this is because a B W are all on the same line and this line sits on an infinite number of planes I could keep rotating around the line just as we did over here it does not specify only one plane