How Do You Calculate the Fly's Displacement in a 3D Room?

[vysero]

I was not sure what the title of this thread should be. This should probably give you an idea of how little I understand this problem:

A room has dimensions 3.00 m (height) x 3.70 m x 4.30 m. A fly starting at one corner flies around, ending up at the diagonally opposite corner. A) What is the magnitude of its displacement? B) Could the length of its path be less than this magnitude? C) Greater? D) Equal? E) Choose a suitable coordinate system and express the components of the displacement vector in that system in unit-vector notation. F) If the fly walks, what is the length of the shortest path? (Hint: This can be answered without calculus. The room is like a box. Unfold its walls to flatten them into a plane.)

First big problem, does it go height, width, length or is it the other way around?

 

[CAF123]

I was not sure what the title of this thread should be. This should probably give you an idea of how little I understand this problem:

A room has dimensions 3.00 m (height) x 3.70 m x 4.30 m. A fly starting at one corner flies around, ending up at the diagonally opposite corner. A) What is the magnitude of its displacement? B) Could the length of its path be less than this magnitude? C) Greater? D) Equal? E) Choose a suitable coordinate system and express the components of the displacement vector in that system in unit-vector notation. F) If the fly walks, what is the length of the shortest path? (Hint: This can be answered without calculus. The room is like a box. Unfold its walls to flatten them into a plane.)

First big problem, does it go height, width, length or is it the other way around?

What have you tried? The displacement vector will be from the fly's initial position to it's final position. The magnitude of this will be $|\vec{d}| = \sqrt{d_x^2 + d_y^2 + d_z^2}$. Some suggestions: let the x, y and z axis represent the length, depth and height of the room respectively. For the later part of the problem, know the triangle inequality; that is $|x| + |y| ≥ |x + y|$, ie the sum of two sides of a triangle is always greater than the hypotenuse.

 

[vysero]

Ok so the displacement vector is equal to the square of the sum of LxWxH^1/2. That comes too 6.42 which is the correct answer. Now my original problem they label the height as 3 m how do I know what the other to values are? Like for instance is 3.7 m the length or the width of the room?

For B) I am assuming the answer is No and therefore I would assume that C) would also be No and that D) would be Yes. For the last two questions I am am a bit confused on where to start.

 

[voko]

Why can't the path be greater?