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A-Level Further Maths: C3-20 3D Matrices: EXTENSION Reflection in the plane y=x - Bilingual Subtitles

So this video is an extension.
Let's say we wanted to reflect in the plane y equals x.
Now ordinarily we understand y equals x to be a straight line when we're looking at 2D.
And if this was my y axis and x axis then essentially it would look like that.
So it is the line that would be going through 0, 0, 1, 1, 2, 3, 3, 4, 5, 5, 6, etc.
And as well as projecting the other way as well, so 1 minus 1, 1 2.
1, 2, etc.
However, y equals x is actually a plane in three dimensions because it's also governing the fact that z could be anything you like.
being anything you like will satisfy that equation.
So, in actual fact, it's a plane.
And It kind of looks like this, I guess.
Okay.
Quite a bit difficult to visualize, but it's a whole plane that's coming through.
And that's still your line y equals x, but this plane is projecting through to the negative z axis as well.
So if I wanted to reflect in the plane y equals x,
think right well one zero zero where's that gonna go well that would get
reflected into zero one zero if that was the case because just like if you
reflected in the line y equals x so we were looking at two dimensions and here
is my reflection line then this point will reflect here, okay?
That's what's going to happen.
So 1, 0, 0 will go to 0, 1, 0.
0, 1, 0, well in a simple way reflect over to 1, 0, 0.
Whereas 001 with it being on the plane
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