Find two points on the line of intersection of the three planes t = 0 and z = 0 and x + y + z + t = 1 in four-dimensional space.

[ghost]

It solves to the line x+y = 1, but will all the points in the line be the point of intersection of the three planes?

[joshuacook]

An intersection of 3 4-planes would be a line.

The intersection of 3 3-planes would be a point.

The intersection of 3 5-planes would be a 3-plane.

Another way to think of it is ... a point is a 1-plane, a line is a 2-plane, ...

[joshuacook]

Just riffing now, but think about how a point splits R^1 in two. A line splits R^2 in two. A 3-plane (or what we normally call a plane) splits R^3 in two.

[ghost]

Ah got it, the 1-plane, 2-plane example helps. Not so clear about R^1, R^2 maybe will get to more about it in the 3rd lecture.

[joshuacook]

R^1 is just a the number line in the reals.
R^2 is the traditional cartesian plane.
R^3 is three space ...

[anindo69]

by plugging t=0 and z=0 we will get in the 3rd equation x+y = 1
now from linear algebra we can do the next step :
1.when x = 0 then y=1 so the 1st point is (0,1,0,0)
2.at the same method x = 1 and the 2nd point is (1,0,0,0)