A hall has the dimensions `10 m xx 12 m xx 14 m`. A fly starting at one corner ends up at a diagonally opposite corner. What is the magnitude of its displacement

Options

A. `17 m`
B. `26 m`
C. `36 m`
D. `21 m`

Explanation

To find the magnitude of the displacement of the fly from one corner of the hall to the diagonally opposite corner, we can follow these steps:

### Step 1: Identify the dimensions of the hall
The dimensions of the hall are given as:
- Length (l) = 10 m
- Width (w) = 12 m
- Height (h) = 14 m

### Step 2: Understand the displacement
Displacement is the shortest distance between the initial and final positions. In this case, the fly starts at one corner of the hall and ends at the diagonally opposite corner.

### Step 3: Use the 3D distance formula
The displacement \( R \) can be calculated using the 3D distance formula:
\[ R = \sqrt{l^2 + w^2 + h^2} \]
where \( l \), \( w \), and \( h \) are the dimensions of the hall.

### Step 4: Substitute the values into the formula
Substituting the values into the formula:
\[ R = \sqrt{(10)^2 + (12)^2 + (14)^2} \]

### Step 5: Calculate the squares
Calculating the squares:
- \( (10)^2 = 100 \)
- \( (12)^2 = 144 \)
- \( (14)^2 = 196 \)

### Step 6: Add the squares
Now, add these values together:
\[ R = \sqrt{100 + 144 + 196} \]
\[ R = \sqrt{440} \]

### Step 7: Calculate the square root
Now, calculate the square root of 440:
\[ R \approx 20.98 \text{ m} \]

### Step 8: Round the answer
Rounding to two decimal places, we can say:
\[ R \approx 21 \text{ m} \]

### Final Answer
The magnitude of the displacement of the fly is approximately **21 meters**.

---