Questions on 3d displacement vectors

In summary, the room has measurements of 4 m in the x direction, 5 m in the y direction, and 3 m in the z direction. A lizard crawls from one corner to the opposite corner of the room, with a displacement vector of 4i+5j+3k in terms of unit vectors. If the lizard chooses the shortest path along the walls, floor, or ceiling, the length of its path is 8.6 m.
  • #1
Sneakatone
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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.
 
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  • #2
Sneakatone said:
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?
 
  • #3
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.
 
  • #4
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.
 
  • #5
never mind its asking for the equation which is, 4i+5j+3k.
n the second part ended up to be 8.6 m.
 
  • #6
haruspex said:
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. :smile:
 

FAQ: Questions on 3d displacement vectors

1. What is a 3d displacement vector?

A 3d displacement vector is a mathematical representation of a change in position in three-dimensional space. It includes information about both the magnitude (length) and direction of the displacement.

2. How is a 3d displacement vector calculated?

A 3d displacement vector can be calculated by subtracting the initial position vector from the final position vector. The resulting vector represents the displacement from the initial position to the final position.

3. What is the difference between a 3d displacement vector and a 3d position vector?

A 3d displacement vector represents a change in position, while a 3d position vector represents a specific location in three-dimensional space. A displacement vector has both magnitude and direction, while a position vector only has magnitude.

4. How is the magnitude of a 3d displacement vector determined?

The magnitude of a 3d displacement vector can be determined using the Pythagorean theorem. The length of the vector is calculated by taking the square root of the sum of the squares of the vector's components (x, y, and z).

5. Can a 3d displacement vector have a negative magnitude?

No, a 3d displacement vector cannot have a negative magnitude. The magnitude of a vector is always a positive value, representing the distance or length of the vector.

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