Finding the Shortest Path in a Vector Space

In summary, the room has dimensions 2.95 m (height) × 4.68 m × 6.19 m and a fly starting at one corner flies around, ending up at the diagonally opposite corner. The magnitude of its displacement is 8.30 m. If the fly walks instead of flies, the shortest path it can take is the square root of the sum of the width and height squared, plus the length squared. However, without knowing which dimension is the width or length, it is not possible to determine the exact length of the shortest path.
  • #1
Neophyte
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Homework Statement



A room has dimensions 2.95 m (height) × 4.68 m × 6.19 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) If the fly walks rather than flies, what is the length of the shortest path it can take?


2. Relevant topic
Vectors


The Attempt at a Solution


SQ RT √(2.952+ (x)2); x = SQ RT of √(4.682 + 6.192)
= 8.30

Part B, I have problems with as I do not know which one is width/length : (

The answer is
SQ RT
√((w+h)2 + (l)2)
But because I do not know which is which I have a slight dilemma... Is there a way to tell?
 
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  • #2
Shorter distance is width.
 
  • #3
rl.bhat said:
Shorter distance is width.

Thank you very much.
 

Related to Finding the Shortest Path in a Vector Space

What are the components of a vector?

The components of a vector are the parts that make up the vector, typically represented by the x and y axes. These components indicate the direction and magnitude of the vector.

How do you calculate the components of a vector?

The components of a vector can be calculated using trigonometry. The x component is equal to the magnitude of the vector multiplied by the cosine of the angle, and the y component is equal to the magnitude multiplied by the sine of the angle.

What is the difference between the magnitude and components of a vector?

The magnitude of a vector is the length or size of the vector, while the components represent the direction and magnitude of the vector. The magnitude can be thought of as the overall strength or size of the vector, while the components indicate how much of that strength is in each direction.

Can a vector have negative components?

Yes, a vector can have negative components. This indicates that the vector is pointing in the opposite direction of the positive component. For example, a vector with a positive x component and a negative y component would be pointing in the fourth quadrant of a graph.

What is the importance of understanding vector components?

Understanding vector components is important in many scientific fields, such as physics and engineering. It allows for accurate measurement and analysis of forces, velocities, and other physical quantities. It also helps in visualizing and graphing vector quantities, making it easier to interpret and apply in real-world situations.

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