What is the polyhedron described by the equation {x} + {y} + {z} = 1

[Scharles]

What is the polyhedron described by the equation {x} + {y} + {z} = 1 ? Justify carefully your answer, and then determine the lateral surface area of this polyhedron.

{x} is modulus of x..

can i know how to do this question ? i can't even understand the question..

 

[epenguin]

What is the polyhedron described by the equation {x} + {y} + {z} = 1 ? Justify carefully your answer, and then determine the lateral surface area of this polyhedron.

{x} is modulus of x..

can i know how to do this question ? i can't even understand the question..

You know what is modulus of x? It is two things - it is x and it is -x.

Following a 'Polya' strategy, try and solve a simpler related problem, or rather subset of the given problems. Let {z} = 0. Then {x} + { y} = 1. So that is four things but altogether what do they make? Then it should be obvious what the corresponding equations with x and z only and then with y and z only make. Following which it should be obvious what your overall equation represents. Try and find then the simplest way to justify this obvious thing.

 

[HallsofIvy]

Break this into 8 cases- the 8 "octants" of the coordinate system.

For any point in the first octant, x, y, and z are all positive. So |x|= x, |y|= y, |z|= z and |x|+ |y|+ |z|= 1 becomes x+ y+ z= 1. That is a plane. Where does it intersect the axes? Remember that this is only in the first octant.

For any point in the second octant, x< 0 but y and z are still positive. So |x|= -x, |y|= y, |z|= z and |x|+ |y|+ |z|= 1 becomes -x+ y+ z= 1. That is also a plane. Were does it itersect the axes? Remember that this is only in the second octant.

Repeat that analysis for the other six octants.