Questions on 3d displacement vectors

[Sneakatone]

A room measures 4 m in the x direction, 5 m in the y direction , and 3 m in the z direction. A lizard crawls along the walls from one corner of the room to the diametrically opposite corner. If the starting point is the origin of coordinates, what is the displacement vector in terms of unit vectors?


-if the lizard chooses the shortest path along the walls, floor or ceiling what is the length of its path?

I do not know where to start please help.

 

[berkeman]

A room measures 4 m in the x direction, 5 m in the y direction , and 3 m in the z direction. A lizard crawls along the walls from one corner of the room to the diametrically opposite corner. If the starting point is the origin of coordinates, what is the displacement vector in terms of unit vectors?


-if the lizard chooses the shortest path along the walls, floor or ceiling what is the length of its path?

I do not know where to start please help.

Welcome to the PF.

The first part of the question is pretty basic. It says that the lizard crawls a total of 4m in the x direction, 5m in the y direction, and 3m in the z direction. Independent of the path it took there is a displacement vector from the start to the end. How do you write that displacement vector in terms of unit vectors?

 

[haruspex]

Can you at least do the first part, the vector for the far corner?
For the second part, imagine taking a paper replica of the room, and cutting it along some edges so that it can be laid out flat. There are several ways top do this, so there's more than one possibility for where the opposite corner ends up in the resulting flat grid, but the lizard's optimal path will be a straight line now. You have to find one that stays on the laid out walls.

 

[Sneakatone]

I got lDl=7 which is correct but it also ask for D=? in meters and i don't know what it is asking for.

 

[Sneakatone]

never mind its asking for the equation which is, 4i+5j+3k.
n the second part ended up to be 8.6 m.

 

[berkeman]

Can you at least do the first part, the vector for the far corner?
For the second part, imagine taking a paper replica of the room, and cutting it along some edges so that it can be laid out flat. There are several ways top do this, so there's more than one possibility for where the opposite corner ends up in the resulting flat grid, but the lizard's optimal path will be a straight line now. You have to find one that stays on the laid out walls.

Great hint, haruspex. I was having trouble figuring out the second part of the question until I saw your hint.